Apple Music won't actually shuffle/play library.
Starting a few months ago, when using Apple Music in the browser I've noticed that even though I have a large library of songs, even when it's on shuffle it will only play songs beginning with "a". It's like it can only find the songs that it can see currently on the screen and nothing that requires scrolling down through the list. I've tried both Chrome and Edge with the same result. The attached screen shot is next playing on my entire collection with shuffle selected.