Just adding my 2 cents and experiences here (have the EXACT same problem as everyone)...
- Have M1 Mac Mini (16GB/512GB FWIW, but don't think it matters). Mac OS 11.0.1.
- Have two Lenovo Q27 QHD screens, identical - they have HDMI + DP inputs.
- Used high-quality HDMI 1.4 and HDMI 2.0 cables, HDMI to HDMI.
- Used TB3 to HDMI (ver unknown, assuming <= 1.4), TB3 to DP, single cables, adapters, dongles, etc.
- Not listing out all the various adapters but they are reasonably high-quality; none are Apple-branded.
- All of these cables, dongles, adapters, etc. work perfectly in a Windows 10 multi-monitor environment.
Problem = upon screen wake (and I even have the "don't sleep when screens are off" checked in the Energy panel), one and/or both screen(s) will flicker, be unresponsive, stay black with no background, etc. This happens when Big Sur sets the monitors to different refresh rates. Sometimes the BT mouse will work well so I can just launch Displays, change the offending monitor's refresh back to 60Hz, and re-arrange, but sometimes not. The other solution is to manually turn off the "black" screen, turn it back on, which triggers something that fixes the issue (still need to re-arrange, but at least Big Sur recognizes the screen).
My conclusion = definitely a software bug/issue. Apple needs to fix this and I presume they will given all the noise/experiences/feedback from the user community.
My work-around solutions = launch Display panel if you can, gather windows, set refreshes back to same Hz, re-arrange. If that doesn't work, turning off the offending monitor and turning it back on has the same effect as plugging/unplugging the monitor's cable and forces Big Sur to re-recognize the screen. Then open Display panel and re-arrange.
This is annoying but at least I can work on 2x screens for now. I turn off sleep which consumes more power of course, but that's a relatively small price to pay vs. just using one screen, and I hope Apple fixes this soon.