Only Location items that Big Sur can detect, and match the Location categories will appear in the Finder sidebar. A damaged, failing, or improperly formatted Time Machine drive may not appear. That external Time Machine drive, on Big Sur, can be formatted differently:
- HFS+ Journaled (case-insensitive) with GUID partition scheme.
- APFS Journaled (case-insensitive) with GUID partition scheme.
I deliberately stated case-insensitive as this is not shown in the Disk Utility options, with Apple preferring to omit the implicit phrase. On my M1 Mac mini, I use an SSD using option 2 above, but on my Intel MacBook Air, I continue to use option 1 on a 2TB mechanical drive. I never enable Time Machine drive encryption, both from personal choice, and not wanting to deal with its overhead.
If a Time Machine drive has mounting irregularities, I would recommend that you run Disk Utility First Aid on it, and get a green successful run, or if not, run First Aid again until you do. Consistent red means replace the drive. Always observe proper drive removal through the Finder (or shutdown), before Time Machine drive removal.