I have the same exact issue too. The button for manually detecting an external display in the display settings window doesn’t appear when I hold down the option key. I tried connecting the same HDMI cable and monitor to another MacBook Pro with Monterey and the second display worked. I also tried putting my iMac to sleep and waking it up. I also disconnected and reconnected the HDMI cable while my iMac was powered up. I also reset the NVRAM and PRAM on my iMac, but still no good. I tried entering safe mode on my iMac, still no good. None of the methods suggested on YouTube or online seem to work. Finally, I downgraded to OS X Mavericks and the second monitor did work on my iMac. This proves that it’s not a hardware issue with my iMac and must be a driver issue. Monterey is trash!