my stone shed got a complete workover several years ago – now stores bikes and used as office. Do have some heating but in effect it sounds exactly what you’re planning.
Quite a bit of insulation worked for me, but then it was intended to be habitable (well, usable) rather than just storage so it was worth it. Ground, wall, roofspace insulated.
Stone walls of about 2′ thick..
Air bricks weren’t used. However in office area there is a stove. Bike store area – no vents, no stove, no condensation either (once the leaking Velux had been sorted).