Maybe not quite the same thing - but have you checked out https://music.apple.com/
Open that in Edge, and then you can install that website as an App into your Start menu.
You can’t download tracks for offline play - but it’s definitely a lot ‘lighter’ than iTunes (and it’s in the same style as Apple Music on your phone, Apple TV, Macbook etc.).
(You can also do the same with Apple TV as well at https://tv.apple.com/)
Y̶e̶s̶,̶ ̶t̶h̶a̶t̶ ̶i̶s̶ ̶e̶x̶a̶c̶t̶l̶y̶ ̶w̶h̶a̶t̶ ̶I̶’̶m̶ ̶l̶o̶o̶k̶i̶n̶g̶ ̶f̶o̶r̶!̶ ̶T̶e̶s̶t̶i̶n̶g̶ ̶n̶o̶w̶ ̶a̶n̶d̶ ̶i̶t̶ ̶d̶o̶e̶s̶ ̶e̶x̶a̶c̶t̶l̶y̶ ̶t̶h̶e̶ ̶s̶a̶m̶e̶ ̶a̶s̶ ̶S̶p̶o̶t̶i̶f̶y̶ ̶C̶o̶n̶n̶e̶c̶t̶,̶ ̶b̶u̶t̶ ̶s̶p̶l̶i̶t̶ ̶i̶n̶t̶o̶ ̶a̶ ̶c̶o̶m̶p̶l̶e̶t̶e̶l̶y̶ ̶s̶t̶a̶n̶d̶a̶l̶o̶n̶e̶ ̶a̶p̶p̶.̶
EDIT: Okay I have to retract my statement above… it’s mostly what I was looking for, as I still can’t pick up a song on my PC (even with iTunes) that I started through the Apple Music phone app. You have to have iTunes desktop app already open so the iTunes Remote app can ‘see’ your media library and then you can go from there. So it really is an iTunes Remote, no integration with Apple Music at all!
Even if I have Home Sharing enabled on Apple Music (the same feature you have to enable in iTunes), it just can’t ‘see’ the library of the Apple Music phone app for some reason.
So still some way to go before it’s anywhere near the functionality of Spotify Connect.
Thanks for the heads up anyway!
I just wanted to say a massive THANK YOU - I’d completely forgotten this app existed and it’s exactly what I was looking for to control one from the other.
I’d really like to see this get to spotify level one day where I can start a song on Mac, pick up my phone and keep playing it on there…
But for now this is a really nice compromise
So I did a quick Google search for ‘Apple Music Windows’ today to see if there were any updates on release timeline. While I couldn’t see anything new about the final release, I did spot that the Windows Store download link for the official AM desktop preview has been reactivated.
Previously when I looked, the ‘Get in Store’ button was missing, as if they had paused the release.
Apple Music Preview - Microsoft Store Apps
Downloaded now and works perfectly for me. Most of the same features as iTunes such as Smart Playlists and local music, but the newer look of the iOS app. Also has support for Lossless for those of you with hardware that supports it!
One downside I just spotted: Because it’s not actually iTunes, the iTunes Remote app suggested above by jzw95 doesn’t work with it. Can’t have it all I guess… 
Also looks like the Apple Music App for Windows is only for Windows 11. If I go to the store to get it, on my Win 10 PC it just says I don’t meet the minimum requirements for it.
Can’t think of anything specifically in Windows 11 that’s missing in Windows 10 that would possibly break this though? (is there extra special encryption available in Win 11 that they might want the tracks to use to stop them being pirated?)
I’ve decided to try out Apple Music for a few months due to a free trial. I normally use YouTube Music Premium (and before that Amazon Music Unlimited). First impressions are that the sound quality is good and it has a nice range of music, however the app and website for YouTube Music are definitely better. I think if I was paying for both, I would choose YT over Apple, but I’m getting it for free so I’m happy to use it.
I’ve moved from Spotify to Tidal and love it 
Apple Music can’t be touched for classical or jazz. It’s also got a lot of really obscure genres (like early 20th century Berlin music hall stuff that my father was quite fond of).
Apple Music Classical is fantastic
I just don’t see why it couldn’t be part of the existing app…
I’d like some of the metadata capability stuff to move across to the normal music app, but can see why it’s stand alone
This YouTube link was posted somewhere else on here which gives an explanation.
For me, the big difference is that the new app adds space between movements. I used to find that the Music app sometimes ran one movement into the next with no space. Not insurmountable, but the main reasons, I think, revolves around discovery.
How do you find the discoverability/algorithms on Tidal?
I actually find it very good. Firstly the music quality through my Sony headphones with the LDAC codec is absolutely noticeable.
After a few days the daily mixes and new and upcoming playlists appeared (I guess after it had learned more about my listening habits) and these are as varied as Spotify.
I found Spotify shuffle to not really be a shuffle, I heard the same 100 tracks or so of my liked playlist. Tidal is surfacing liked songs I haven’t listened to in years
I miss Spotify Connect, but Tidal’s option works for Chromecast, it’s just not as smooth.
Overall I’m happy with Tidal and I’m staying. Even bought the family plan.
This article is excellent – explains that and also delves onto the strengths and weaknesses of Apple Music Classical:
Upon using Apple Music a bit longer, I have gotten used to the app and website and they really aren’t that different to YT Music. It is also recommending me similar songs to the ones I got on YT Music. The lyrics are better as they actually move with the song, and you can get music to play in the background on XBox Series S. The audio quality is also clearly better. However, the student plan is £1 more expensive. Don’t know whether it is worth it once my trial ends (I know it is only £12 more a year, but that is still something I can spend elsewhere).
Clearer on desktop or mobile apps?
Did you move your music lists over to ytm with a tool ?
If this is in response to me, mobile is definitely better. I don’t think I could tell a difference on laptop.
Despite moving from Amazon, to YouTube, to Apple, I have yet to use one of the methods to move my playlists over. I don’t listen to that many different things so it isn’t much hassle just adding them back. Plus, Apple and YouTube have recommended me many of the songs I missed anyway.
It was to you, discourse doesn’t show the reply icon when replying to the last message but you should get a notification icon, but other users wouldn’t know so that’s annoying.
I was asking because at least on browser, ytm used to play in lower quality than what was available on the mobile app.
If a song isn’t available on ytm it will play it from yt on the native yt audio quality which is worse than ytm, and often I found those tools would add the wrong version of the song, or the music video listing so the ytm app would play the yt version even when it had the high quality music only version.
So it has been almost a week and I am blown away by the mixes that Tidal has created for me (and the tracks on the radio stations it has suggested for me). I thought Spotify discoverability was really good, but Tidal is surpassing it.