Everything but the coordination server is open source. But you can selfhost this part yourself: https://headscale.net/

Tailscale is (like) a VPN, but traffic will go through their servers.

That's wrong. In a peer to peer VPN the traffic should not pass Tailscale infrastructure.

See their docs: https://tailscale.com/kb/1094/is-all-traffic-routed-through-tailscale

Must you give your mustard to everything?

Another very fast and folder based system would be mStream: https://mstream.io/

It works very well, also good mobile apps (Android + iOS)

Flame is not actively maintained anymore. Have a look at this fork which offers support for categories: https://github.com/fdarveau/flame :::

This is the right answer.