Interesting, I use both Messages and a few third-party messengers, and I wouldn't say that Messages is integrated more deeply with iOS, in the way that e.g. Safari and Mail were for a long time (before you could re-associate http and mailto URLs).

The share sheet just shows my most-frequently-used messengers, as well as direct contact names for my most important contacts, no matter what messenger they're actually on.

The only thing I can't yet do on my third-party messenger is initiate messages from my Apple Watch, but that's presumably due to a lack of a native watch app more than anything.