Same problem. External SSD for Time Machine, APFS formatted. Lost access with Monterey and can't get it back.
I did find this:
https://developer.apple.com/forums/thread/680500?answerId=676624022#676624022
Not formatted in ExFAT (APFS), but after entering command was prompted for password but had no ability to enter ($ sign was pre-entered.)
anotherapplefan
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