I have the same problem. External SSD drive for Timemachine, APFS formatted. Creating the initial backup worked, then was running for some time and all of a sudden it can't be mounted anymore. Might be that it occurred after a reboot, I usually never reboot my Mac. The same external drive was working before Monterey smoothly for over a year. After the update the Timemachine backup could not be finished because of some strange file conflict. Whatever, I reformatted everything and started from scratch and now I am in this new situation. I think there is a sever bug somewhere in Monterey.