Mac mini's HDMI port stopped working after upgrade to Big Sur

I have 2 monitors connected to my 2018 mini; one via HDMI, the other is Thunderbolt-to-HDMI. After upgrading to Big Sur all was fine for a day or so, and then I rebooted - since then the HDMI connection no longer works. If I open About This Mac and go to Displays, it only shows the one screen (i.e. the one using Thunderbolt-to-HDMI). I tried resetting SMC (https://support.apple.com/en-ca/HT201295) but that made no difference.

I have tested the various combinations: I used the Thunderbolt-to-HDMI cable with each monitor, and they're both fine, so I know the monitors are ok; I tried a different HDMI cable (taken from my Xbox setup, so I know it works) and About This Mac only sees the one monitor, so I can rule out the cable; that leaves me looking at the mac mini itself and wondering if it's a bug in Big Sur or a hardware problem which coincided with the upgrade.

I can't find any mention of a bug disabling HDMI, but now I'm at a loss for what to do next. Is there something else I can test before I resort to taking the mini to the Apple store? It's my main machine for working from home so I really don't want to be without it while they investigate.