Confirmed the HDMI cable is fine (it works with another computer and the other monitor).Upon first boot into Big Sur after the update, one monitor wasn't working (the one with HDMI).

Monitor 2: USB-C/Thunderbolt to DisplayPort I have a dual 4K monitor setup which has worked fine since I bought the computer. I just updated my Mac mini 2018 to Big Sur, and the HDMI port no longer works. Have re-started a couple of times since and it's all good - the only strange thing is that during start-up the Apple logo and progress bar do odd things in terms of size and screen location - presumably as different drivers are loaded during start-up The Apple and progress bar started out on the USB screen, but switched half-way through to the HDMI screen. Then re-started, and (surprisingly) it all worked. Reset the resolutions and monitor arrangement. Then added the second monitor over USB-C. I was the default resolution and background, but I fixed those. It took longer to crank up than normal, and there was no Apple logo and progress bar, but after a couple of minutes, the screen lit up. Then tried switching off disconnected all monitors connected just one using the HDMI-HDMI cable. I re-started a couple of times.Searched the web got frustrated. Just black screens and (apparently) no output signal from HDMI. Tried multiple cables and switched between monitors. Initially on upgrade to Big Sur, the HDMI port did not work. (Mac Mini 2018 + 4k over USB-C + 4k over HDMI).

Hdmi not working mac 2016