irc if you don't require any bells and whistles. matrix if you want attachments and encryption. zulip if you're running a company.

Downloads some forum software and runs in it on a VPS or similar?

There are also some FOSS Discord clones in various states of maturity

I don't mean to advocate for Discord (they sure don't need it!) but if the requirement is to host an exclusive space for a dozen people, Discord does that.. you just make a "server"/guild and only invite trusted friends.

This doesn't solve any of the other problems (what happens when Discord enshittifies? Is it acceptable that Discord updates basically every single day? Is it OK that they constantly advertise video games in the form of little notifications saying "stream 30 minutes of _____ to a friend and unlock an avatar for your profile!"?) but it does seem to solve the 'how do I have a platform for my friends and I to talk" one.