Brigandine's menu music is pretty good, and it has to be because you spend forever in those menus. It's relaxing, and you need that contrast sometimes to the more bombastic themes of some of the nations in the game.
Of course that's a tactical game. Usually in a regular JRPG it's just best to just carry the regular background music into the menus to keep you emotionally connected to what's going on in the story.
Like if they cut you off from "Life will Change" in Persona 5 with a menu music as you're heading in to fight the boss, I think it'd really ruin the mood.
I'm pretty sure it doesn't count for this question, but it did bring to mind Cadence of Hyrule where it had 16-bit renditions of the music play when you bring up the menu. And yes there were shopkeeper variants of THOSE tracks as well if you brought up the menu near him.