Does signal still require me to share a phone number?

It does (or at least did, when I was using it). It only requires it for registration, so you could even use a disposable phone number, but regardless it is a nonsensical choice for something that could aspire to be a general-purpose chat application.

The server is open-source so you could host your own server -though that's not very practical due to the client situation (not really a variety of configurable ones, so you'd probably need to change/package/distribute the official).

I used Signal for more than a year. Unfortunately compared to Keybase's chat, it is buggy, slow and lackluster in functionality.