YT Music really is odd. I pay for YT Premium and so have played with it a few times but it feels rather ill-suited for its purpose… as you say, the video streaming heritage is quite evident. Apple Music, Spotify, Tidal, heck even Amazon Music last I tried it have much more music-oriented UIs.

YouTube is also actively hostile to third party devs in ways that at least Apple isn’t, somehow. Third party Apple Music clients have existed for years using official Apple-provided APIs, which YouTube isn’t going to ever allow even for paying customers.