Different companions have their own planned stories but they're all in a 'it'll happen when it happens' state.
- Cait has a quest with a whole fuckton of implications but most of it is simply outside the scope of the game (ie, we're not going to Jassira and we're definitely not going to Mareth) so that's more something that would influence the ending(s) if anything, but per the design doc she's got more of a role to play in the story in the future.
- Brint/Brienne are getting massively increased content in Khor'minos so progressing the story is progressing their development.
- Atugia's content has yet to be written.
- Berwyn's expansion is being worked on right now.
- At least some content for Kiyoko is being gated behind Kinu's questline, which is currently incomplete but which is part of a massive subplot that could probably be a game unto itself.
- Azzy presumably has a good bit of future content planned (you can see a hint of it if you look at the parser guide) that just hasn't been written yet.
- Hints have been dropped for future Arona content but the plot hasn't really gotten to the point where it matters yet, and the fact that she has chieftan/exiled states means that it would take more time to write for her to account for both. Savin's specifically mentioned eventually going back and adding content for the latter.
- Quin's plotline runs in parallel with the plot concerning Tollus' cult so advancing the plot is advancing his development.
- Ryn has a still-unfinished story and the latest patch points the way towards its next steps but it hasn't been time for that to happen yet.
Expansion on that plotline is gated behind whenever we get to Tychris, which is not the devs current priority. Hint: Khor'minos.
Perhaps less than you'd think, since Kas decided it was time to skip town right as the CoC1 Champion was kicking down the door. We know that the 'canon for purposes of CoC2' ending features the 'Lethice purified' ending and the other demons defeated but not killed. Consequently everyone was kinda busy at the time and it's possible that nobody else was paying attention to the portal and Calla got ignored by the demons. Aileh certainly doesn't make any mention of Calla if you're on the route where she shows up.