Hmm around 18-24 months ago I gave Apple Music a try but found there were TONS of tracks from my personal library that the service would not play. Perhaps they’ve improved things since then? I went all-in using Plex as a personal media server since then and while the UI isn’t as nice, it lets me steam my personal library anywhere from any device.

You may have chosen not to subscribe to iTunes Match which is the feature which gives you access to Apple's servers to host all your songs instead of keeping them strictly local. At least that is how I understand it.

I’m pretty positive I did this actually as I recall the ‘match’ service being an additional fee. I was stoked to have a cloud option for my library as I’d been maintaining it for 10+ years and always griping about backups. I recall it working great for tunes I’d purchased from Bandcamp but when it came to tracks which had been in my library for many years (originating from many different sources), they simply didn’t show up in my library. Again- this was around 2 years ago so it’s possible this is no longer an issue.

I’ve since setup a Synology NAS with Plex and it’s mostly great.

You don’t need to subscribe to Match if you’re an Apple Music subscriber.