After purchasing a "Certified HDMI" cable and still having no luck on my Mac mini M1 after the update with Monterey 12.0.1. I found that changing the refresh rate to the lowest setting corrected the issues on my primary screen (Sceptre 24") with the second screen unplugged. But my 2nd screen(Sceptre 34") only had a black screen when plugged in (Hooked up though a long USB-C cable to a cheap amazon multi hub adapter to HDMI). Hooking the Sceptre 34" up as a primary HDMI to HDMI with the new certified cable would work for a bit then white noise and just cycle back and forth between working, white noise and black screen.
Long story short after hours wasted and trips to the store for "Certified" cable I found that the original setup that always worked before the update also works perfect after the update when the refresh rate was turned to the lowest setting for both monitors.
Click the apple in the top left > System Preferences... > Displays > Display Settings > Refresh Rate
Set the refresh rate for both monitors to the lowest number available.