I downloaded Big Sur yesterday and have been dealing with this annoying problem for the last hour. I'm not very sure this fix will work for everyone but it's the last thing I tried and it randomly started working. 2018 MBP (Big Sur official), iPad Pro 12.9 3rd Gen (14.2).
Go to iPad bluetooth settings and connect to MacBook through Bluetooth.
After this my iPad Pro 3rd Gen showed up but gave error when trying to connect to Sidecar.
I disconnected MacBook Pro from the iPad bluetooth settings.
Restarted MacBook.
On restart iPad Pro still showed in display settings and when I went to connect it worked.
My only guess is that by connecting the two machines through the iPad bluetooth settings it somehow allows the MBP to recognize the device in other ways. Good luck!
bkismobile
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