There’s already a play button at the top if you do not remove it in the settings (Hide top button row in lists).
You keep repeating songs but as I try to explain those artists that you can’t play do not have any songs associated with their name. So there’s no song list or songs to play for them.
What there is a list of album and those albums have songs. But those are not the songs from the artist, it could be anything that appears on those albums.
If artist X is album artist of album Y but album Y have 10 songs from artist Z, then you will play 10 songs from artist Z.
If you really want to play songs by the artists then you need to fix your tags.