I'm doubtful that it is related to GDM, I've seen similar reports of dcn20 issues on Plasma as well. But for the heck of it you can always try installing an even older version of GDM that we still have kicking around in stable repo. No guarantee it'll work but hey, you can always roll it back if it doesn't work.
In terms of whether or not you should switch away from GDM + GNOME Shell and to Budgie, it's your system so you're welcome to do whatever you want with it. What I will say is, so long as it isn't too much of a PITA for you to keep using it as is, it might be valuable to stay with GDM since the issue is most easily reproducible with it, and thus it's easier to validate if / when it is resolved elsewhere (e.g. kernel).
Anyways, the installation command:
sudo eopkg install https://mirrors.rit.edu/solus/packages/shannon/g/gdm/gdm-3.36.3-52-1-x86_64.eopkg
No guarantee GDM 3.36.3 will work (regardless of whether or not these dcn20 issues existed, strictly because there was lots of other software that was changed in the GNOME Stack that GDM may rely on, like GNOME Shell itself).