Same here on all fronts about distractions. I can't tell whether when people talk about listening to music while working/studying: (1) they mean music with no lyrics, (2) they are unserious and okay with their work being constantly interrupted, or (3) they can resist thinking about the lyrics.
Some work may allow for seamless pivoting between work vs. enjoyable distraction, e.g., a clerk, but I often hear about people listening to music in other contexts.
The work is not always to implement some complicated algorithm. Sometimes it is just routine work. There's already so much noise outside so having the music give something for the brain to latch on instead of having to react to all those other stimulus. For me it's a playlist that I know very well, which then becomes background noise.
Sometimes I listen to music without lyrics like surf or gabber. Other times its genre music like northern soul or punk or familiar music where the lyrics are so familiar or vacuous/cliche that they don't distract. I wouldn't listen to really lyrically focussed music like singer songwriter stuff generally. So I think there's a spectrum rather than just instrumental music vs everything else.
Some work may allow for seamless pivoting between work vs. enjoyable distraction, e.g., a clerk, but I often hear about people listening to music in other contexts.