I mean, I dont know in game but some legends say he's a son of a Muse or something iirc, so his power over the music maybe comes partially from that?? Since Idols can have mortal kids it's not impossible. Persephone saying he's so much more than a muse may also be some respect for a skilled person [kinda like Arachne] who honed their craft rather than an indication that bard is some sort of magick position to have? Just hypotheses but I agree I am curious as hell about the in-world explanation