Similar issue here too. When plugging in either usbC or usb3 external drives - my experience shows this is a flip of the coin whether Big Sur recognizes and mounts the drive or not. I think particularly that the exFAT partition format type has something to do with this issue. Apple's Disk Utility also has a hard time displaying what the actual formatted partition is. For instance, I took an Apple drive over to my Ubuntu Linux machine, erased the drive and repartitioned it as exFAT, removed it and plugged it into my MacBook Pro on a USB adapter and it didn't recognize the disk even after several unplugging and replugging attempts. So I rebooted. It saw the external drive, but showed it still as an Apple Journaled APFS partioned drive. That's odd I thought, so I unmounted it, removed it and plugged it back into my Ubuntu Linux machine. Lo and behold it was exFAT not APFS. What's going on with Apple's Big Sur? Hard to say, but it looks and feels like a bug.