My vote is for matrix. Yes you need to get an account, but Matrix can be encrypted, and I have had a very nice time using it. I have heard that moderation isn't the best, though, So that's one minus. Another worry is a good instachat might detract from the people who use the forums. I've looked around the Battle for Wesnoth project and literally no one's on the forums.
Another thing though, and It's something some people might not want to hear, is we might want to have discord. I know the privacy policies are gross, and it's not open source etc. etc. etc. I hate discord probably more than the average person myself, but from what I can see this project has only a handful of people working on it.
I'm not saying 0 A.D. is dying or anything, but it's tiny for a game of this quality and size. We need to try to make this project a bit more accessible for the "new kids". Moving to git/Gitea is a plus, because people won't have to deal with a weird/ outdated version tracker. But we also need an easy way for people to get into the community. Most people don't want to have to download a new app, get another account, figure out an entire new interface and all that stuff. The communities for minetest, endless sky and even battle for wesnoth (which none of them look as cool as 0 A.D.) are bigger than ours. What's the big difference? Well they all use GitHub for version control, (but we have mirrors and that doesn't really help) but they also have discord.
Again I'm not saying Discord is amazing, I really hate it, but we might want to grit our teeth and have a discord in some capacity in order to get more people. We can have bridges and stuff and backups and other methods but I think if we want 0 A.D. to flourish it might be our best bet.
In summary, if we need an instachat my personal vote is for Matrix, but I would strongly suggest we as a community swallow our pride/take a hit on our lofty OSS values and embrace discord to a certain extent so we have more than two dozen people in the community. I know more people visit, but it seems like its only Gurkan Kan Wowgetoffyourphone, me, Vantha, and Stan and like 3 others are the people who post more than once or twice a month. And I'm sure contributing code is something similar.
(Also, why does the forum text field say my content needs approved by a moderator?)