Elements: Can't see tags on photos moved to new storage device

1 - Your tagging is recorded in the catalog
2 - You can 'write metadata to files' from the File menu. Then, your tags, notes, captions and ratings are available without the organizer for other softwares.

So, if you want to transfer your library (photo files folder tree) as well as your catalog, you have to use the 'backup and restore' process described here:
https://helpx.adobe.com/photoshop-elements/kb/backup-restore-move-catalog-photoshop.html

This process is the only one which can both copy your catalog folder and keep the links updated for the new drive. It is also the only one which can keep your albums, version sets, stacks and creations available for the new drive. Writing metadata to files is optional because working with the catalog only may be much faster. It's useful or even necessary if you want to share with another software (even your Explorer/Finder) and it's an additional safety step.
Note that you can copy or move your catalog folder from your Explorer/Finder. You find the catalog folder location from the menu Help >> System Information.

Thanks for the help Michel!