Does YouTube Music allow non-premium accounts to download their own uploaded music to their device for offline use?
I haven't tried this but according to Upload your music - YouTube Music Help, you can

You can play uploaded songs in the background, ad-free and offline - even if you are not currently a YouTube Music Premium subscriber.

(Emphasis added)
You would need to use a computer to upload (you cannot use YouTube Music mobile app). Once uploaded, you can view in the app. You can verify this by uploading a few songs