monogame is pretty much the continuation of XNA although they have added more stuff.
There is another framework called FNA that I've not used personally but I've heard it tries to match XNA exactly while monogame is a bit more forward looking. So FNA is good for porting forward your older XNA games.
Because I had to check this myself: Monogame is not tied to mono! It claims to support dotnet 8, so it looks suitably current and maintained.
It is annoying that Microsoft had their own perfectly adequate game framework which they binned at one of the transitions https://en.wikipedia.org/wiki/Microsoft_XNA