Jabuffum,
Thank you for checking those settings. There is another software update available for Big Sur. The latest is macOS Big Sur 11.2. You'll want to update to see if that resolves this issue. Also, if you haven't already, restart both computers and attempt to AirDrop again.
You can also create a test user to confirm that this issue is system wide and not an issue with-in your specific user.
Set up users, guests, and groups on Mac
Log out, sleep, wake, restart or shut down your Mac
How to update the software on your Mac
If you are still unable to detect your Mac mini after following those steps, you may be able to reach out to Apple Support for further assistance here: Get Support.
Take Care!