.

Is there a readymade docker install ?

There's no point installing it as you can't use it. It's just provided for transparency. Not to run a home server like with matrix.

Yes it is: https://github.com/signalapp/Signal-Server

Telegram's backend is closed-source.

Yeah, but your instance can't communicate with other Signal server instances, so it's pointless.

No it's not pointless. It might just be pointless for the "socializing with random people" use case.

Yes it is, because you can't join two servers at the same time. You run your own server, I run mine and we can't communicate until one of us decides to drop our whole network and join the other server.

That's fine. As I mentioned, the use case you are talking about makes this pointless.

Someone that needs a special set of phones to be able to communicate securely and not be reliant on a publicly run server? Here's a non pointless use case.

I'll let imagine who might run something like that.