Look I know that “the Doctor can hear the soundtrack” is possibly pointing toward some big series-long arc.
But in the meantime, I like to imagine that the music represents the Doctor’s alien senses, with the translation matrix turning it into music to make it comprehensible to us, the human viewers. Like when we hear ominous music or a familiar motif, the Doctor is sensing bits of the web of time, or using some other wacky timelord(ish) sense that we don’t have. The Doctor isn’t exactly breaking the fourth wall, but that’s the closest thing the TARDIS can use to approximate it.
It reads as genre savviness because that’s what it would be like if you kind of know the future. Not necessarily in exact detail, not enough to pick the right action every time, since there are countless possible futures/pasts for any non-fixed point. But the Doctor still has way more information about any given time than a non-time traveller would — and seemingly more than a human time traveller would either.
