How To Restore Music Library from Backup

This is from a iTunes Windows support article, but is likely relevant.

An XML file appears to be reliant on the referenced music files being in your library already. It was not designed to recreate a library.

Only the music files physically present on the SSD were still there.

That seems to be the design.

It's not quite clear to me why the Apple Music tracks I had added earlier can't be re-added to the Music library after a restore of "Music Library.musiclibrary",

Did you download the tracks or were you streaming them? You can use Apple Music on both ways. If streaming, the actual music file was never on your Mac.

Here are 2 songs on my Mac. One is local and one isn't.

I'm curious which data in other cloud based Apple services can be deleted so easily, and not be restored from Time Machine backups...

Kind of a loaded question.

If you keep in mind the design of all iCloud services, you should be fine. iCloud is not a backup service, in that you go back to a certain point in time like Time Machine does. It is a syncing service, which keeps content the same across subscribed devices.

It does this in pretty much real time.

There are some locally cached files with iCloud Drive where you can actually use Time Machine to retrieve them. In other words, the local files are removed when you remove them from either iCloud or a subscribed device like an iPhone. Now you can go back to the last Time Machine backup and retrieve that folder or any file in it. If you don't mind digging, I hear you can do the same for Notes databases, Contacts etc, as they are all held locally as well. Photos is a variable, and depends on where you store your original files.

So, as I suggest, if you do not consider iCloud as a backup, you should be fine. It is a tool of convenience more than anything. And a good one IMO.