My external display stopped working immediately after upgrading to Monterey on day 1 (v12.0.1). Specifically, didn't display anything but was still recognized in System Preferences → Displays.
The fix in my case was to change the display's "Refresh Rate" from "Variable" to "60 Hz" (though I'm sure any of the fixed frame rates in the drop down would have worked).
Since Big Sur didn't offer the "Variable" option, I'm 99% certain the problematic setting was written by the Monterey upgrade routine, since it (correctly) detected that my monitor (an Acer B77 marketed as supporting ActiveSync) theoretically supported Variable refresh rate. But given the gap between theoretical & actual support for Variable refresh, it would have been nice if Monterey only overwrote that setting after confirming with me that the display still worked, as I never would have thought to check that setting if it weren't by luck that I happened to be looking for the new Variable Refresh Rate feature the first time I connected the external display.
I'm not sure where the problem is. I connect to the display indirectly via a Belkin Thunderbolt 3 dock and don't have the necessary adapters/cables to re-try the Variable rate option via a direct connection, so it could be the Acer display, the Belkin dock, Monterey itself, or some combination thereof.