In the Movies tab, you’ll see shared media files that are tagged as Media Kind: Movie. Untagged media files will appear in the Home Videos tab. Could that be a cause of a discrepancy?
I checked and no, there's nothing misfiled in the Home Videos tab.
Could it be that (some of) the media files are on an external disk that is currently not connected?
The files are on an internal disk that is always connected.
Could it be that the Library has recently been moved between disks?
The Library has not been moved at all.
Could it be that some the media files on the Mac are there, but not (yet) added to the library in the TV app software?
All files were previously added to the library (with artwork, notes, etc.) and, as mentioned, were previously visible and playable until the latest update. I can still find them in my computer's library but the TV app software no longer displays them and they do not show up under the Computers app on Apple TV. They are, quite simply, gone from the Apple TV environment.
Could it be that more than one computer is in the home network?
There is only one computer on the home network.
Is it loading the intended library?
As mentioned, it is loading the intended (and only) library on my computer. Only a fraction of the intended library now appears, whereas before the entire library would load without a problem.
I do appreciate the reply, despite it leading to no answers here. The fact that I must now resort to rebuilding my entire movie and TV library under a third-party media home sharing system is more than annoying. It signals that Apple intends to restrict its Apple TV users to content they rent or sell.