It's not just about counting the number of panels. Carrot was indeed in two panels in this week's chapter with the Straw Hats. And a few last week. And the week before. It's the consistency with which she's shown in the same panels and the nature of her interaction with the crew. It's little details like this one:
Carrot reacting with surprise to Robin's morose theory about dead babies rising from the ocean to clam the ship of the Beast Pirates. It's a small detail, but stuff like this matters. Carrot interacts with and blends into the crew in a way the other Musketeers simply do not. And I'm talking about Carrot as a whole, not just in 978.
I don't think she needs a tragic flashback. In fact, I don't expect her to have one. We saw Pedro's death happen real time. He passed on his will to her. I believe Pedro would have joined the crew if he hadn't died. That's the 'surprise'. "Treetop" Pedro, who has a tendency to climb to high places and accompanies the Straw Hats on their mission to rescue Sanji is a natural choice to become the crew's lookout. He believes Luffy will be the 'Light of the New Dawn' (I've seen this referenced a few times in this topic; The 'Light of the New Dawn' is not a prophecy about Wano, but the end of the current epoch in One Piece world history which began with the end of the Void Century), but then we find out he has tragically already lost the majority of his lifespan to Big Mom. Carrot stows away because she dreams of adventure and Pedro dies. His dying words are to pass on his will to see that Luffy becomes the 'Light of the New Dawn' (ie Find One Piece and defeat the darkness that inhabits this world).
As has been mentioned by others in this topic, the 'lookout' position is something the Straw Hats are currently managing by means of sleep deprivation and just like Pedro, Carrot shows a natural proclivity toward this position. The whole bit about the Straw Hast needing a helmsman never came up before Whole Cake Island. Prior to that, people had speculated that Jimbei might be the helmsman based on the fact that he helmed the Battleship leaving Impel Down, but there were no big 'master helmsman' moments until the escape from Whole Cake Island. Oda had a key and he designed the lock into which it fit. He created a problem to be solved by Jimbei. No one ever predicated Jimbei joining based upon his skill as helmsman and no one pointed at Franky at the helm on the two occasions Jimbei was previously aboard Sunny as evidence to his lack of ability to fill that position.
There was limited panel time in this chapter - in any chapter. The whole point here was not to call out attention to Carrot's skill as a lookout. Let's not pretend that Jimbei's official role is anything but ancillary to his broader character traits. Usopp needed to snipe some guards, so instead of it taking multiple panels of Carrot loudly calling out that there are guards, Usopp did it discreetly. It was an Usopp moment. It's not a mark against Carrot just because it wasn't an Usopp & Carrot moment. If you even think about the logistics of that scene, it wouldn't have made sense for Carrot to jump to the top of the crow's nest and yell down that there were guards up ahead if the point is to show Usopp quietly dealing with the situation without anyone noticing. Quiet being the operative word here.
Every other companion who has sailed with the crew for multiple arcs has done so with an express purpose - aside from perhaps Johnny and Yosaku, but that was over two decades ago at this point.
The entire Baroque Works saga built toward the liberation of Alabasta. Vivi recruited the help of the Straw Hats and sailed with them for multiple arcs in the quest to stop Crocodile. She was offered to join, but stayed behind out of obligation to her country. Vivi not be aboard the ship, but she is considered a Straw Hat.
Kinemon, Momonosuke, and Law fill a really similar role in the quest to take down Kaido and liberate Wano.
Hatchan and Camie guided the crew to Sabaody and hung out with them on Fishman Island, but didn't sail from island to island. They also served an important role in the arcs in which they appeared.
What was the point of Carrot coming along to Whole Cake Island? Couldn't her role have been easily absorbed by Pedro? If the whole point was to have a 'Sulong' moment to build anticipation for Wano, Pedro could've done that. Pedro's big heroic sacrifice could have been going 'Sulong' aboard Sunny in place of Carrot. By past convention, Pedro is the one who was built up to be a Straw Hat. He had a tragic flashback where he lost half his life to Big Mom. He had a unique quirk (suddenly climbing to high places) which made him a natural fit for the lookout position. He accompanied the crew on an important mission sailing from one island to the next. He had an innate belief in the crew's importance to the world. The expected outcome would have been Luffy beating up Big Mom and getting her to return Pedro's lifespan so that he could join the crew. But that's not what happened. Carrot stowed away and accompanied for the sake of adventure - because she has never left Zou and wants to see the world. Luffy wasn't near strong enough to defeat Big Mom. So instead, tragically, Pedro sacrificed his life to help the crew escape - and passed his will on to Carrot who picked up his mantle. It was Carrot's 'tragic flashback' moment in real time.
Oda has featured her consistently in group shots / moments together with the Straw Hats even if she has been less prominent. The Minks as a whole were in hiding during Wano Act II so her relative absence is easily explainable. On the cover of Volume 88 (the 'heroes' cover for the arc; comparable to 21, 43, & 77), Oda featured Carrot in panes of broken mirror along with the other Straw Hats while arc allies Chiffon, Bege, and Pudding are in the background. Carrot had big character moments in helping the crew defend the ship against Big Mom's fleet and a touching farewell to Pedro with Sanji at the end of the arc.
As I said, number of chapter appearances is not the metric to evaluate her chances. Carrot has appeared in 85 chapters, tied with Rob Lucci for the 18th / 19th most frequent number of appearances in the entire series (I counted cover story arc appearances). I bring this up because the number of chapters Carrot has been around has been brought up a few times. Yes, she has been around for longer - she has also been present in a large number of those chapters and played a major role, comparable to the rest of the Straw Hats, during Whole Cake Island. She has now sailed with the crew for three consecutive arcs, a distinction only held by Law, Kinemon, and Vivi, the latter of whom is considered a Straw Hat despite her absence from the ship. Law is a captain of his own ship, a D., and an a formal ally to Luffy in this multi-arc saga. No one has seriously considered Law a viable candidate to join the Straw Hats because his role in this story has been abundantly clear. Despite the fact that he is not a Straw Hat, his alliance with Luffy has essentially elevated his status to a primary character from secondary character for the majority of the New World. In live action terms, he was elevated from a 'recurring' character to 'main cast.' I'd argue Kinemon was to a degree as well, though I think it's important to note that Kinemon took a major back seat during Dressrosa and didn't even appear on the 'heroes' cover (volume 77) for that arc. Kinemon's purpose in traveling with the Straw Hats was again, buildup for Wano. The purpose for his voyaging aboard Sunny has always been clear. The past six months is the most focus he has ever gotten in the story despite having been introduced seven years ago. If Carrot's role is to go back to Zou and fade into obscurity, it's not at all clear why Oda would have her play such a prominent role and tag along aboard Sunny for multiple arcs.
I'd also draw attention to the direct parallels which can be drawn between the Baroque Works Saga and the Kaido Saga:
Punk Hazard - Whiskey Peak
Dressrosa - Little Garden
Zou / Whole Cake Island - Drum
Wano - Alabasta
On the first island of the Grand Line / New World the Straw Hats meet a new ally Nefertari Vivi / Trafalgar Law, Kinemon, and Momonosuke, who sets them on a mission to take down Warlord of the Sea / Emperor of the Sea, Sir Crocodile / Kaido. They set out from the first island, Whiskey Peak / Punk Hazard and arrive at Little Garden / Dressrosa where they face off against an underling of Sir Crocodile / Kaido. Luffy defeats 'Mr. 3' Galdino / 'Joker' Donquixote Doflamingo which puts a wrench in the plans of the big bad. The crew then set out for their ultimate destination, but their course is diverted when one of the crew - Nami / Sanji is put in jeopardy. The crew changes course, arriving on Drum Island / Whole Cake Island, inadvertently becoming embroiled in the affairs of that island, but picking up a new crew mate, Chopper / Carrot, in the process. They finally arrive at their ultimate destination and assist Vivi / The Kozuki Clan and the Heart Pirates in taking down Sir Crocodile / Kaido, a despot pirate who seeks to exploit the resources of the land for their own personal gain.
The course of the adventure has been largely similar structurally to the Alabasta arc. There are obvious differences - Wapol was defeated, Big Mom followed on to Wano. My point is, the Baroque Works saga takes a little over a hundred chapters start to finish. It begins in chapter 101 if you count the Twin Capes and ends in 217 with the surprise of Robin stowing away aboard the Going Merry. The Kaido / Big Mom saga is similar in structure, but the individual arcs have gotten way longer. The earliest seeds were really introduced all the way back on Thriller Bark (Charlotte Lola, Samurai Ryuma, Oars, Captain John, Moria, Kaido and Wano introduced by name). You could say the story was initiated by the final scenes on Fishman Island. But I'll consider the start of this saga formally as 654. Here were are 324 chapters later with the end of Wano still a long way off. The scale has been increased fourfold. So yes, Carrot has been around for more chapters without a 'formal invitation', but these events are also playing out over a longer period of time. It would have been very unnatural for Carrot to say 'let me join too' during Jimbei's big moment just from a storytelling standpoint. That was Jimbei's moment. He has already agreed to join twice and stayed behind due to his prior commitments. He was introduced into the story over ten years ago. This was a long time coming and that moment was rightfully focused entirely on Jimbei. And then the celebration was conveniently put off until the end of the arc - where there will be two new members to celebrate.
Last thing I want to tackle is the idea of Carrot joining the fleet. It seems contradictory to simultaneously diminish her significance by pointing to any appearance of Wanda and Sicilian as equally important - to try to prove that she isn't going to get any significant story time and yet expect that somehow, she'll get enough focus to sail off on her own at the end of the arc. Carrot, who has no experience at sea, will become captain of a ship? The same Carrot who was amazed that it would take more than half a day to sail from island to island? And the same Carrot who isn't anywhere near a leadership role by rank among the Minks will command them as their captain to join the Straw Hat Fleet? Beyond the fact that I don't think Carrot has demonstrated any desire to become captain of her own ship and that she likely does not have the reputation or experience among her people to command such a position, the end of Dressrosa made clear that the Seven Captains who presently comprise the fleet will be the cause for a major world incident in the future. While I do not doubt that more will be added to the ranks of the Straw Hat fleet in the future, I do not believe it will happen before this 'major incident' - otherwise it would not be specifically those seven who cause an incident. Also worthy of note is that Sabo gave them all Luffy's Vivre Card, which Carrot does not have. She has never met the other Captains, but it's expected she'll just go out to sea and find Bartolomeo? Why would she not tag along with the crew to whom she has already grown attached if her dream is to see the world and to help Luffy become the Light of the New World in order to respect Pedro's wishes? It's just a really roundabout way to accomplish a goal.
If anything, I'd expect Carrot to simply stowaway aboard the ship again when they set out from Wano if she isn't formally asked or invited. Or it could be a simple 'get on board dummy. you're already one of us' moment like Usopp received. I mean, she already invited herself onto the adventure once and is shown frequently together with the crew, so I'm not sure why anyone expects that Luffy needs to invite her. Sometimes people impose these really word and unnecessarily rigid rules upon Oda as if the Straw Hats must follow a strict application process. Mozu and Kiwi told Luffy to invite Franky to join. Robin stowed away aboard the ship. Jimbei and Luffy became friends and then parted ways for two whole years before reuniting on Fishman Island. He agreed to join, but delayed formally sailing together with the crew twice. Nami is the first one to invite Chopper if memory serves correctly. Zoro is the one who tells Usopp to get aboard the ship. Luffy is the only one present when Sanji formally joins. Luffy asks Brook to join before even getting to know him. Nami is still officially part of Arlong's crew for the first three arcs of her tenure as a Straw Hat. Vivi has it all and doesn't sail away with the crew at the end (though I believe she will return to them in the future). My point is, there's no one size fits all approach here. Every Straw Hat has their own process of joining which is right for their character and their situation.
I'm not saying Carrot is 100% going to join. There is a chance she stays behind. But it would have to be with good reason. I do not see 'joining the fleet as a captain' as a viable option here unless Wanda, Sicilian, Inu, and Neko all bite the dust this arc. That said, I think there is a very strong chance she will join the crew. I'd say I think it's very likely for a myriad of reasons outlined above.