Maybe its just me, but I have this feeling that the reason Carrot isn't really getting much spotlight this time, is because she is more or less already a part of the crew and has been with them for a long time now, but it hasn't been made official yet within the story's ongoing plot. In fact, the moment she stowed away on the ship towards Whole Cake Island secretly, that was pretty much the defining action and Luffy pretty much accepted her without much issue. It explains also why people constantly see her among the Straw Hats, besides a few exceptions here and there.
He did the same exact thing with Robin, who also stowed away and joined out of her own free will, and Luffy was okay with it despite their past encounters.
Everything else that surrounds the "requirements" of a new crewmate joining just happened in real time with a small flashback emphasizing her connection with Pedro. She just needs one final small push now, although it won't really change much in the grand scheme of things. In other words, Carrot has already pretty much joined in a similar fashion to Robin, and Luffy has been okay with it, despite not really acknowledging it yet in full. At the end of Wano, I could literally see Luffy going to pull a Usopp here, in which Carrot is about to say goodbye, but Luffy asks what she's talking about, and tells her to just get on board because he and his crew already consider her as nakama due to the time they have spend together.
Also, unlike Yamato so far, Carrot has met all of the Straw Hats pretty much, even though its not always made obvious and has bonded with some of them. I think that counts for something, even though its not much I admit. Yamato in turn, has only met with Luffy and Franky. Everyone else has yet to see her in action. Does all of this hurt Yamato's chances? No, because I recognize her potential, and so far, the story is giving off a lot of strong hints of the character joining the crew.
If so, then Yamato is the latest one to join if the story goes on its current trajectory. However, Yamato still needs to get a opponent to fight, because everyone else of the Straw Hats, including Carrot is being set up with getting a face off, with Brook and Robin still pending, but if things go as people predict, they will face off with Black Maria, while Sanji may go up to help out Luffy and Zoro against Kaido.
As for the idea for Yamato being the crew's stonemason….I can see that happening. Its a pretty legit profession and as Syphin already mentioned, has lot of connections to the story. Its also why I think she will have the mythical zoan of the Byakko.
The White Tiger namely represents the element of Metal in mythology, which works nicely with a stonemason profession, but also, as mythology tells, the White Tiger will only appear when the emperor rules with absolute virtue or there is peace throughout the country. Momo may still not be officially the ruler of Wano, but he's getting there and I believe he will bring the peace of Wano as such, and with that, the White Tiger will appear. Its why, to me, its no surprise that Yamato just so happens to be there with him at this moment, and seeing as the Byakko is a mythical creature, Oda would want to save its reveal until the time is right to show off Yamato's full power.
https://en.wikipedia.org/wiki/White_Tiger_(mythology)
Other than that, that is all I have to tell for this topic. For the rest, its just a waiting game for me. I like Yamato as much as I like Carrot, so whether both join or just one of the two, Im content either way.