I do find it amusing that GPM closing down made Apple Music the best music experience on Android. For how I browse and listen to media it's far better than YouTube Music was for me - not to mention it actually looks really good.
Personally, I listen to most of my music by Album, then by all albums of an artist only in my library, and finally by playlist. YouTube Music made the default organization (atleast when I tried it) by viewing the entire artist, and viewing individual albums was multiple layers deep. I also kept running into music on there having their licenses renewed (I think?) and they would be disappear from my library. I'd have to go back and re-add the albums. I just became frustrated enough I had to search for something else. I just really like the layout of My Library -> Artist (play or shuffle all) -> Albums (play or shuffle all).
Can I listen to Apple Music on my desktop on a web browser while being logged in to Apple Music on my iPhone/Android? The last time I subscribed to Apple Music (back in March or April 2023), it didn't allow being logged in and playing music on multiple devices simultaneously.
On a single account, no. You cannot listen from multiple devices at the same time. You can have multiple logged in, but only one can be actively playing a time. I've swapped between my phone and my desktop -- and occasionally you'll get a popup that "only one device can be listening at a time" but it usually just takes dismissing & clicking play again to get it to refresh. I think if you have a family plan the limit is 6 devices or something, but don't take just my word for it.
You cannot listen from multiple devices at the same time. You can have multiple logged in, but only one can be actively playing a time.
This wasn't my experience. I was logged into Apple Music on my iPhone and whenever I logged into Apple Music on my web browser, it did play music for a while but then music would stop playing randomly and I was told something similar to what you mentioned about only one device being active. I had to reload the page to make that warning go away but it came again after a while. This was when Apple Music wasn't being used on my iPhone, it was just logged in.
I don't see how Apple Music can be considered a useful streaming service with this limitation unless one doesn't possess more than one computing device (literally just an iPhone, or just an iPad, or a just a desktop/laptop and nothing else). Sounds absurd. This isn't an issue with either Spotify or YT Music.
I use iTunes on the desktop, but I've only ever had it happen when I've been listening to music on my phone a minute or two prior. I've never logged out on either and if it was outside the few-minute window I was never prompted with that popup. Sorry it didn't work for you, and that would probably be a dealbreaker for me, but fortunately that's not something I run into.