UnifiedPush has been a thing for a while, see the official website: https://unifiedpush.org/
With this blog post, we† tried to clarify a few names. Feel free to point out things that are still unclear, the documentation is pretty much a WIP.
UnifiedPush aims at replacing the push notifications mechanism provided by Google services with something independent, that anyone can self-host or any OS can provide without compatibility issues. It does require small adjustments server-side and client-side for applications assuming Google services.
There is also a Matrix room at #unifiedpush:matrix.org and a Mastodon account at https://fosstodon.org/@unifiedpush
Note: we'll be monitoring this topic for a while, you don't have to reply to this thread.
† karmanyaahm and S1m are main authors