"File seems to be corrupted" in iCloud Music Library

There are quite a few tracks (and whole albums) in my iCloud Music Library that played perfectly fine for the last ten years.

Now that I tried to back it all up and download them, Apple Music suddenly tells me that "The File seems to be corrupted" when I try to download.

After that it also won't play anymore.

What can I do here? It's like Apple Music randomly deleting a portion of my music library and no way to fix it. Even worse, I now can't access files that I had for many years.