iTunes on Windows; Can't access music after downloading app

Uninstall Apple Music, and Apple Devices/Apple TV if you have installed either of those. When any of these three apps are installed iTunes will be limited to managing audiobooks and podcasts. After they are removed you should be able to select music from the media selection tool once more.

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Assuming that you've selected to sync all songs from iTunes one would expect everything to be copied over except songs that are in the cloud (likely not relevant unless you subscribe to Apple Music/iTunes Match), not where they are expected to be (will show an exclamation mark if you attempt to access), or unchecked. You can make a smart playlist with a rule such as Checked (or Ticked) is false to reveal all unchecked items. Occasionally specific combinations of metadata and options in the library and the device can cause tracks not to show up where they are expected to, but still be there. E.g. appears within compilations rather than under the expected artist. Try searching on device to see if a track you think is missing reveals itself.

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Sounds like you're signed into Apple Music but your library isn't syncing properly. Try this:

In iTunes: Go to Edit > Preferences > General and make sure iCloud Music Library (or Sync Library) is checked. Restart iTunes.

In Apple Music app: Make sure you're subscribed to Apple Music and signed in. If songs are greyed out, it could be a subscription or network issue.

Reauthorize PC: In iTunes, go to Account > Authorizations > Authorize This Computer.

If still stuck, sign out and back into your Apple ID in both apps. That usually refreshes everything.