*checks* I was wrong, it's $10/month, or $15 for a family plan (family plans let you have ~6 people with their own logins, playlists, history, etc, and simultaneous streaming on different devices).
https://music.youtube.com/music_premium
https://www.spotify.com/us/premium/
I did confirm that your example album is on YouTube Music, and yes, it would play the entire album straight through without ads. You can control exactly what plays via your phone by setting up a saved playlist or your in-the-moment queue, or you could get a smart speaker and just tell it what to play.