Older Playlists in Music are empty (no tracks).

Great. You might take a look at Managing your Mac media libraries - Apple Community. In the long run it will be easier to backup your library and move it to a new drive or computer at some point in the future if you get the library into a standard layout of a Music folder that contains your .musiclibrary package and a Media folder that contains all media connected to the library. Right now I suspect you are using a dated .musiclibrary package from the Previous Libraries folder, which may well now contain another Previous Libraries folder, which can complicate things if you ever had this issue again.

tt2

Are you attempting to open an older library directly in Finder? If you do this Music opens with whatever library was previously selected. To change libraries you must hold down the Option key as you launch Music and then click the Choose Library... button.

If you have a subscription to Apple Music or iTunes Match and Sync Library is enabled then whatever library file you open it will update to the current state of your iCloud Music Library if your computer is online. You can potentially go offline, open an older library database, export playlists, then go online and import the exported lists. The success rate of this process may depend on how much of the content is stored locally and isn't part of the Apple Music catalog.

tt2