If you're using a keepass database, Keepass2Android can natively sync with many cloud options including self hosted and generic ones, even without specific "companion" apps. That's what I use. In my case, it's backed by my NextCloud, but it used to be Google drive before.
Just also sync the file on your PC, merging changes from different clients is part of the keepass database format and "just works".
Also VaultWarden works great if your can self host it, but I prefer keepass for a variety of features and integrations.
You can't have it both ways. It's hard enough to get people to switch to signal, or least also use it next to other messengers. Now imagine they'd have to connect to multiple servers to talk to multiple people. Possibly everyone connection details. Even if that's done in the background, you have to somehow get the connection registered once, discovered if you will.
Anything and everything you send through their server is end-to-end encrypted. Some people hate on the phone number being required to create an account, but it's also the reason it works at all: anyone in your contacts who also has signal you can talk to. Phone numbers are an international standard. If course this also has downsides...
Finally what you're asking for exists. NextCloud has "talk". Which is essentially a messenger app, it's built in. Go use it. I have a NextCloud instance and I don't use it either. What's the point of having an app I can only use to talk with people so close to me that they're in my NextCloud with an account already?