It is not super unusual for a file in the pool to not have a Tempo setting (or even a wrong one, always double check) - so that is not abnormal. But I’ve never seen where it can’t be edited.
Try using Backup Project to copy the Project and all its audio files to an entirely new location. Are those same files locked there too?
I’m still suspicious about the OS permissions. Are you on a Mac or PC (fyi this is why we encourage folks to include their DAW specs in their signatures so no one needs to ask )
You implied that some of the files do have their tempo set. Are you able to modify any of those?
See the file Scratch03bb29 in the pool screenshot attached. I can modify any file that has a tempo other than “???”. Also posted permission screenshot.