Privacy

Well then, literally almost ANY chat daemon you can install in any Linux will just do. And there are loads!

If you want to pay a provider to do that or rent a cheap Vs and do it yourself is another thing.

So if some guidance is all you need that's fine and something I'll gladly provide. Rocketchat - as someone else already posted - is relatively recent but also quite modern due to this, running in browser, app or mobile (but quite the overkill für a handful of people).

Any really old IRC based daemon would not require any resources by today's standards and still run perfectly for your case. But it's very old standards might not fit your expectations.