I am upgrading my hard drive so I am going to do a fresh install of my operating system. What files do I need to save from my present PS elements 2020 install so I can maintain my setting and catalogues etc?
The situation is exactly the same as migrating to a new computer.
You have to 'move' your catalog and media files following the full backup and restore process from the organizer. A full backup on an external drive, followed by a restore on the drive and master folder of your choice.
your media files are stored on another drive, that's good. It does not matter if that drive is internal or external.
Just look for the location of your catalog: menu Help >> System Information. Copy that folder to the same drive which stores your media files (outside of the master folder of your media folder tree). Test that you can use that catalog copy to work with your media just like with the original catalog.
I don't think you'll have issues with the cloning. Even in that situation, the catalog copy would work normally.
The danger with cloning is in a particular situation. If someone had both the catalog and media files in the OS drive, it would be tempting to re-install the OS and programs on a new (small) SSD and to use the older drive as another drive (external or internal) still storing your media folders. In that case, the old drive will have a different drive letter and will not be recognized by the old catalog. I have not tested it myself, but logically, cloning the OS drive also containing the catalog and media folders changes the identification of the new drive. All your files are 'disconnected'. That's why you are good because your media folders are on a separate drive; and copying the catalog folder lets you test how that will work even before starting the cloning.