Today’s update: I experienced a crash very quickly when running on the non-fallback kernel, but then rebooted through it and been running for almost 11 hours with no crash at all 
Still not trusting anything.
In case somebody finds this helpful, some people at this post Issue with mesa after [Stable Update] 2021-04-09 - #2 by AlbertoSalviaNovella claim that there’s a venv that, when set properly, solved many of their GPU issues (while playing games, tho). We may give it a try.