I usually do not comment on forums, but let me try to offer some help!!
After updating Catalina 10.15.4 to Monterey 12.3.1 in a 2019 MBP 16"(intel), I bumped into a similar problem. After restarting the Mac several times, disconnecting the reconnecting the wires and trying almost all the tricks I could find on the internet, they didn't work. Finally, I decided to tinker with display preferences by lowering the Refresh rate to 47.95 Hertz and changing the colour profile to "Colour LCD," then after 20 to 30 seconds, voila it worked. Returning to refresh rate back to 60 Hertz will render your display useless again. Hope this will be helpful for those who bumped into similar challenges. For those whose colour profile and refresh rate are crucial to their workflow, the display I'm using, DELL E2214H, 21.5 inches (1920 X 1080) shows Colour Profile: Display P3 and Refresh Rate: 60 Hertz which was there by default, which is decent right?. Hope this will work for you too as we eagerly wait for the update to fix the mess.
Sounds fishy, there are no external display issues reported for those using Studio Display