It didn't explain that from now on your own music library isnt yours anymore, at least not on their software.
It's just way too invasive - I thought we are getting the regular, although enhanced Music app (yay, finally I can queue music!) AND apple's own spotify integrated into one seamless experience. What we got instead is Apple's own spotify service with an added possibility to store songs you previously bought on iTunes.
This is almost entirely just flat out not the case... HOWEVER, the caveat to that is the same as it has always been: without iTunes, your ability to actually manage your music on your device is minimal to nonexistent.
I noticed you said "my PC is currently being fixed" and my suggestion to you is wait until it is fixed.
The problem ultimately is that Apple's Match service (and the Music equivalent) is a fucking pain to set up. ONCE setup though, fortunately it is almost entirely "set it and forget it". Your library is still intact (provided you didn't wipe it from your PC or such) and if, once your PC is back, a attempt at setting it up again still isn't as successful as you'd like, you can give it another shot. Basically Match is, try, correct, retry, correct, retry, correct, until you have it. I am NOT defending it.. It's a fucking pain, but in the end when you get it working it is unquestionably way more versatile than google music. On top of that, with your desktop iTunes back you then have full control again of your library (including music added to it through Apple Music).
I would almost argue that Apple Music is the ONLY service out there for true music enthusiasts/completists. It's the only one that gives you the combined full control over metadata of tracks, albums, combines your purchased/owned library with the streamed library, provides curation based on both your streamed selections as well as owned selections, etc.
Anywho.. Just wait til you get iTunes back. For someone interested in the management features that help managing a 15,000+ library well beyond any other service, you need iTunes which frankly sounds like a big part of the problem you're currently experiencing. As for the Match problems... Ugh... It took me around 3-4 days to get my ~10K library into Match 3 years ago. Was it frustrating? Like you wouldn't fucking believe. Have I had a problem with it even one single day since then? Nope. The upside to going through the Match hassle three years ago even transferred over to Music, as Apple seemingly just transfers users' existing Match libraries over to Music seamlessly and flawlessly. So that's my attempt at a silver lining. It is worth the horrible setup. Thankfully you only have to do it once, after which it actually works 100% as advertised.
Oh the other silver lining I alluded to earlier. If your initial Match from your PC doesn't work well enough, it actually does nothing to your library. Most people will back up their libraries first. If you care about your play counts and ratings you should definitely do this. If the upload fails, wipe everything out, correct what failed (if it's a matching issue) then restore your library and go again. If you don't care about play counts (don't remember if ratings are in the ID3 or not) you don't even need to do that. Just delete the song from iTunes/iCloud, choose "Leave original on disk", then reimport the song.
Based on everything you've stated, I really don't feel there's a comparable service to what you want. I certainly never found Spotify anywhere near it in terms of combining libraries, Google is not as robust as Match, and having two services to access my "entire" library always seemed awful. Apple Music is the only service out there to meet that need. Ugh... But yeah, get your stuff up there and then it runs near flawless.
edit - so now I actually have a user question. A song is playing... You can pull it up in now playing.. Please tell me there's a quick shortcut to get to the whole album from here... Right...? Right!?! Because I can find it.