Maybe others will relate? I'm not a headphone person but always have music playing in the background on speakers — often at a fairly low volume so it is easily ignored, talked over.
I find without the presence of external music I will have a song playing in my head instead. And generally the same song for hours (!). So I suppose the external click-track freezes up my mind somehow.
In case anyone cares, my "playlist" is local music I've purchased over the decades — maybe 4 or 5 days long? In my "lab" (man-cave, I suppose) I have a shorter, streamed playlist on the stereo that is looping over new music that I am currently "auditioning". The songs that make the cut are purchased and added eventually to the local playlist that plays elsewhere.
You might enjoy Oliver Sacks' book Musicophilia: Tales of Music and the Brain. You're not alone in your experience.
*And height limits.