Why are my radio songs not showing in Apple Music Radio history?

When playing "My station" under "For you", the songs that play, don't appear in my played songs history. The "previous track" button doesn't come to your aid either.

So many times the algorithm has found brilliant tracks only for me not to have added them to my library or favourited them. To add insult to injury, this usually happens through my excitement, and consequently, hitting the skip instead of star button on the Touch Bar 😒.

[Re-Titled by Moderator]