It looks ugly so far, but I have found a related thread "
Elements Organizer 14 and 2019 on Mac OS Keep Losing Files Because They Switch to Time Machine Drive"
Comments here and in this reference thread point to Organizer and Time Machine incompatibility.
I searched for just one file by name in my computer and found it, in the directory where I knew it to be. However, when I look at info in Organizer the location path is different and includes the name Time Machine. So the file has not been moved. Organizer, however, has a different name for its location.
I am not a Mac user, but I can tell you that it has always been advised not to use Time Machine with the organizer. I can't find the most pertinent discussion from last year by a Mac user expert.
Apart from explaining the incompatibility problem, this user explained that the solution is to setup Time Machine not to cover all your disks in your computer and to store the catalog and the media files on a separate volume, not referenced in Time Machine.
The organizer has its own backup mode.
I hope Mac Expert will come and explain the process to setup Time Machine to ignore the catalog and library.
I right now I'm faced with a disconnected files that I can't get to, which I mention here just in case someone looking at this thread has the solution to that issue. No files were deleted. So presumably I can find them with a search.
<<this user explained that the solution is to setup Time Machine not to cover all your disks in your computer and to store the catalog and the media files on a separate volume, not referenced in Time Machine.>>
My MacBook Pro has just one disk. I guess your comment means I must break it into a volume that Time Machine is constrained from addressing.