"When I went back to my original catalog, there were no pictures"
It appears you did not 'open' the original catalog. You probably opened a new empty catalog.
"...so I imported them back in again from the Pictures folder."
If you import again, you lose everything in the (not found) original catalog.
"However all the Albums are gone and so are many (but not all) of the tags and ratings."
That was to be expected: you don't recover anything from the original catalog, only tags, captions and ratings which have been copied in the media files themselves.
I am running Windows 10 Professional with all the pictures (and other data) moved to the C:
drive using sysgen during the windows install. The Catalogs seem to be stored in C:\Programdata\Adobe\Elements Organizer\Catalogs. I have backups of all the stuff in my user directory from the C: drive but the Windows File History doesn't appear to back up the Programdata on C so I have no current backup of the catalogs.
I have no idea why you did that, but there is nothing Windows can do to move or backup anything like this. Please explain.
The organizer has its own backup and restore procedure. The catalogs are folders stored in the default location you have mentioned, unless you have stored them anywhere else in 'custom' location.
Here are my questions: Am I correct about the location of the Catalogs.
Yes. You find the location in the menu Help > System Info of the organizer.
There are appear to be other copies of catalogs elsewhere on the system but none that are anywhere near current.
Quite possible. Older versions or older catalog folders. What did I do wrong? I have had ongoing problems with the Catalog and have had to redo Albums , tags and ratings before.
Most probably because you tried to import files instead of converting the catalogs. Remember that only the catalogs store the information about albums, stacks and version sets; those metadata cant be written in the metadata section of the media files themselves. Where are the following stored: Tags (It appears they are stored in the individual file metadata but why are many of them gone) Albums
Those data are ONLY stored in the databases of the catalog folder. For instance albums are just sorted playlists of a collection of items. They don't contain any image, they point to the media identifier in the database.
You can't access that information unless you are smart enough to use an sqlite management software in the main database of the catalog folder (catalog.pse18db for PSE2020).
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