Hello istemper,
In my opinion music syncing is by far the most convoluted part of using Apple devices recently. There are about four ways to do it but each has its own restriction.
Starting with the manual sync, you may be using the wrong method based on your macOS. Sync your iPhone, iPad, or iPod using your computer - Apple Support.
Also, If you were subscribed to Apple Music or iTunes Match you might just need to turn sync back on since re-downloading the app. This would mean deleting the app did not delete your music it just removed the access to your library.
"Turn on Sync Library
With the latest version of iOS, iPadOS, and macOS, Sync Library is turned on by default. If you turned off Sync Library, you can turn it back on. Just follow the steps below for your device.
On your iPhone, iPad, or iPod touch
- Go to Settings > Music.
- Turn on Sync Library. If you don't subscribe to Apple Music or iTunes Match, you won’t see an option to turn on Sync Library.
If Sync Library is updating or turned off, you'll see a message at the top of the Library tab in the Apple Music app."
This is different completely but depending on how the music was downloaded originally you might be able to Redownload music - Apple Support and since you cannot see them to re-download this may be helpful. If there's an issue when you redownload apps, movies, or other content from Apple - Apple Support
I hope this is helpful,
