What to use to insulate exterior walls of room in a balloon frame house

This is a 2nd story bathroom (gutted to studs) in a 120 year old balloon frame home in the midwest US. Zone 6, pretty rainy, home is vinyl siding with house wrap over original wood cladding on studs. So from inside this gutted room, you see the back of the exterior cladding in the stud bays. This means there is a lot of air and sound leak to the inside.

From what I understand, this was intentional in old houses so that the wall cavity could dry out if needed. The last thing I want is to create a mold problem in this house that has stood strong for so long in a flood zone.

Is mineral wool ok? If so, do I also need to install a vapor barrier? I’d love to air seal but understand this could be a bad idea in old construction?

There is no exposed knob and tube in either of these walls and I will be installing fire blocking.