I had similar issues but was able to find a workaround. Its by no means a real "fix" and I obviously can't guarantee that this will work for everyone.
My workaround was: go to "Display" within "Settings" and turn on HDR.
I just got my M1 Mac mini today, and i immediately noticed my monitor switching on and off repeatedly during the "Migrate from another Mac" process. It didn't really bother me at the time, but after everything was set up, i noticed the monitor would show what looks like radio interference, especially when displaying dark colored content. The monitor stays on, but the brightness would flicker around the edges.
I tried changing cables, I tried different ports (HDMI-HDMI, HDMI-Thunderbolt, HDMI-Display port, Thunderbolt-Display Port etc.) but nothing solved it.
So then I started messing around with the display settings and turned on HDR and BAM, no issues whatsoever. My monitor supports HDR, and its a bit straining on the eyes but certainly a lot better than screen flickers.
Hope this helps someone...