I develop a self-hosted service designed to do exactly this! It's not quite finished yet, but it's at the point where enough functionality works that it can be used for testing.
https://github.com/connervieira/HealthBox
The docs/USAGE.md file gives an overview of how HealthBox works. Feel free to poke around in the other docs/ files as well.
Whenever I question Signal on Reddit, I get downvoted to hell.
In terms of privacy, I still vastly trust Signal over WhatsApp, Snapchat, etc. But they've been sketching me out more and more lately. First was them making Signal dependent on Google services. Then there was them threatening to sue projects that attempted to create forks of the project without said Google dependencies. Now it's them not disclosing the source code for their server side software.
In their defense, the client is still mostly open source, but they need to stop acting like some savior for privacy when they are so hostile to open source.