time machine stopped working

I have been using Time Machine for quite some time now, backing my mac both to a Time Capsule and to a third-party external drive (home and office). A few weeks back, I noticed that I cannot retrieve backed-up data anymore. On both drives, Time Machine seems to be backing up regularly, as it should, but Entering Time machine just shows a stack of windows going back at most 48 hours, and anyway I can't navigate to these windows, nor retrieve anything.

Trying to access the data directly from the disks doesn't work either: I can mount the disks alright but if I try to open the .backupbundle, I am told that I can't open the disk images, resources currently unavailable.

How can I regain access to my backups? Thanks for any advice!

[both my OS (Catalina 15.7) and my TimeCapsule systems seem to be up to date.]