There is no way to see full album or song credits on YouTube Music right now. But that may be changing soon. An eagle-eyed reddit user spotted a change to the song menu that now includes an option to view song credits. Tapping the overflow menu next to each song will bring up options with a ‘View song credits’ to see the composer, producer, songwriters, and performers listed by the music metadata provider.
Source: YouTube Music Song Credits Coming Soon? — The Evidence