How do notifications work in the official Telegram Android app (Play Store vs Site version maybe)? Does it have the same mechanism as Signal, which only recognizes the presence of notifications via Google services, but sends them via its web socket service?
Yes, if you assume an absolute worst case scenario with Signal, it is a small fraction as bad as the known problems with Telegram.
Which I think says more about how good it is, than how bad it is.
Self hosting, meanwhile, opens you up to a new world of pain. Are you a professional grade website administrator? Are you a professional grade security expert? Do you trust your friends to be at least as good as you? If you don’t, are you planning on sending your data to their servers? What platform are you using? What server are you running for it? Etc.