They released a beta patch a short while ago.

https://forum.paradoxplaza.com/forum/index.php?threads/battletech-1-0-1-release-notes-beta.1092920/

Has anyone been able to access it in Galaxy?

I can't see beta channel, tried restarting Galaxy and nothing new shows up in the Channel drop down.

[Update]

It appeared now. Maybe I was just too eager and it wasn't ready. :P

I used the beta for a while last night and it seems slightly better but the game is still highly unstable for me.

Yeah me too.

I think it was rushed out to fix the crashes some people were having when starting the game, but they didn't do anything about the stability / massive resource usage issues yet.