About Carrot not appearing much lately, I have a small theory on why and what her purpose/arc is. I don't think she's going to join, but I'm certain her character arc is going to be addressed and resolved at some point.
Here are my thoughts:
Wano is not just Kaido's arc. It's the conclusion of the "Yonko Saga". It will close a lot, and I really mean A LOT of threads that have been left dangling for the past ten or so years. Not everything, some threads will go on next saga. But the major ones, the ones linked to Kaido and Big Mom, will get resolution.
WHat makes me think this?
First, the way the past arcs that form what I call "Yonko Saga" interweave Kaido and Big Mom together, despite their stories starting apart.
I believe the first arc of the Yonko Saga was Punk Hazard. But the saga actually started in the Fishman Island epilogue.
Big Mom Act - Fishman Island Epilogue: Here we are introduced to Big Mom. We knew Fishman Island is her territory already, but near the end of the arc we find out that Jinbe is under Big Mom as well, and that's why he couldn't accept Luffy's request to join. We also get the first glimpse of Pudding, and get to know Pekoms and Tamago, who will later tie into Zou. Luffy picks a fight with Big Mom, and the Tamatebakko with the bomb trap is given to Big Mom. All setup for things that will only pay-off much much later.
Kaido Act - Punk Hazard: Here we have the whole alliance with Law to take one Yonko, who we later find out to be Kaido. Caesar is introduced (who's essential to Kaido's plot, but later we find out was also linked to Big Mom, and will be the first key to tie both Yonko's stories together). Kid/Apoo/Hawkins alliance is also introduced. Kin'emon and Momonosuke introduced. First mentions of Kuri, hints of Oden, Ancient Giant experimentation on Punk Hazard hinted.
Kaido Act, but with a bit of Big Mom - Dressrosa: THis continues Punk Hazard, and Doflamingo is directly linked to Kaido. Most here will lead into Wano, but there's a small bit of Big Mom when her pirates appear to retrieve Caesar, forcing the "Curlybrow team" to move on to Zou before the end of the act. Its conclusion sets Kaido in collision course with Luffy/Law, as well as leads to the capture of Kid and Hawkins joining the Beasts Pirates.
Kaido/Big Mom Act - Zou: While Kaido is moving the strings on the key events on Zou, it's the Big Mom Pirates that arrive there and take Sanji and Caesar. This is the point when the Kaido/Big Mom plots first interweave perfectly, leading to what will happen later in Wano.
Big Mom Act - Whole Cake Island: The Kaido plot that dominated the Yonko saga so far halts so Big Mom, introduced way back in the saga's prologue, can finally have her moment and is led to Wano later. We pick back Jinbe's story, Pudding gets the spotlight, characters initially linked to the Kaido story (Pedro and Carrot) get their beef with the Big Mom Pirates. The Straw Hats that were absent from Dressrosa (Kaido act) get conflicts with Big Mom instead (Nami - Zeus/Lola, Brook gets some kind of relationship with Big Mom, Jinbe leaving Big Mom, and so on). Carrot gets her big motivator going forward (Pedro's sacrifice and last words to her).
Kaido Act - Wano Act 1: Before Wano actually began, we were all sure it would be Kaido's arc, and the conclusion of the "Kaido saga". But no, since the start of the arc, we start moving Kaido and Big Mom together, so their stories become one. Big Mom threatens to go to Wano, and offers Kaido an alliance for the first time. The threat of an Yonko alliance sparks talks of "Rocks", which we didn't know what it was back then. Aside from that, there's no Big Mom in this act yet.
Kaido Act, but Big Mom is also here - Wano Act 2: The Big Mom Pirates arrive. There's two reminders during the act that Kaido and Big Mom used to be in the same crew (first when the Big Mom pirates are discussing what to doafter they are thrown down the waterfall, then when Beast Pirates are talking about a captured Big Mom). Big Mom surrenders to Queen (thought it's made to appear like she just fell sleep) because she wanted to be brought to Kaido. Kaido and Big Mom clash, but end up allying instead.
Kaido Act, but Big Mom is still here - Wano Act 3: We find out the story of Rocks, and suddenly the Kaido/Big Mom threat becomes the "Return of Rocks". While Big Mom is often treated like a joke, we are always reminded that she's no pushover. The Big Mom Pirates almost arrive, but are delayed, so the Beast Pirates remain the sole threat. However, Big Mom and Perospero are kept as movers and shakers, but often fade into the background so Kaido and the Beast Pirates get the most attention. We get hints that Kaido expects betrayal. Big Mom seems to imply ulterior motives to Perospero. We are briefly reminded that Pudding may be able to read poneglyphs (if her lineage awakens). Carrot gets some small attention - coincidently in the same act as the Big Mom part of the story gets smaller attention in comparison to Kaido. Carrot's arc words (Pedro's words) are repeated. Carrot then fades into the background again, waiting her resolution.
So, what I think the future holds?
I've been saying (and mocked) repeatedly that the Big Mom Pirates will arrive, and Perospero is the key to that. I think Oda reserved Act 3 to deal mostly with the Kaido side of the story, while everything Big Mom related is kept waiting for now, since dealing with both threats at the same time would make everything slow down to an even worse pacing. I feel Kaido's forces will suffer some defeats now, enough to appear like we will winning. Then the Big Mom part of the story comes to the forefront, and Act 4 begins.
Act 4 will be the big, fast-paced conclusion to both stories. This is when both Kaido and Big Mom, and their crews, are defeated. We get revelations about Rocks. This will also bring complications from WCI. For instance, I think Pudding's story will pick up again, as strange as it seems. That's the point I believe Carrot gets the spotlight back and finally resolves her character arc.
Act 5 is the epilogue, when we close almost everything we have been dealing with since Fishman Island epilogue. Jinbe finally joins and gets his party. Both Sanji's and Zoro's stories from WCI and Wano also get resolution. Carrot and Yamato situations are resolved. All the info from ponelglyphs from both WCI and Wano are unveiled at once.
That's what I'm betting on happening.