Strange- so it seems indexing is working, it can't be an inappropriate or non-recognised file or file type 'cos it's picked up after manual indexing.
You could obviously repeat what you've done with an mp3, for example: if Cortana finds the mp3, and Groove doesn't.. well.. hard to imagine what's going on.
So, try re-registering Groove, and if that doesn't work, uninstall it and reinstall it.
Uninstall Groove Music:
Get-AppxPackage *zunemusic* | Remove-AppxPackageor-
Step 1. First of all, download and install CCleaner for Windows 10. And then click on Tools and then click Uninstall tab to view all installed apps.
Step 2. Now right-click on Groove Music app, click Uninstall, and then click OK for confirmation to uninstall the Groove Music.
Step 3. Reinstall: launch the Windows 10 Store.
Step 4. Now in the Store app, type Groove Music in the search box to see Groove Music in search results. Click on it.
Step 5. Click Install button. If the store is showing that the app is installed msg instead of Install button, close the Store app once and run it again.
Step 6. That’s it! Now clicking install button will download and install the Groove Music app on your Windows 10 PC.