Professions is something I like with WoW, although Legion was a resounding MEH on that front.
I do not think professions in wow have music? The gnomes have their zink zonk plonk music, and it certainly gives association to nutty engineering, but otherwise…?
So, let’s start with engineering. I had some trouble finding something engineering, but you can’t go wrong with a tractor. Not as fancy as real gnomish construction, but I think gnomes (and goblins) would love this (the comments are gold, too):
Blacksmiths can enjoy this. There are choral versions too but I think this fits better as game music.
Alchemy. Check the potions before drinking 😉
Leatherworking. When the singing is 100x better than the video. Platforms shows up in a lot of studios in the 60s. Kitschiculous (kitschy and ridiculous)
Cooking… sing about “go steady”. Endearingly old fashioned lyrics.
Can’t think of anything for enchanting, so here is one more for the jewelcrafting (with added shine)
Herbing. Not really about flowerpicking but the Burns poem uses an rose as metaphor and Eva Cassidy was a very special singer.
Hope you find something to your liking.