Too many questions to give a simple answer. What are the building and lot line restrictions where you live? Building costs between shed and addition may be equal, but I'm sure running electricity (maybe water for a potty?) to a shed will cost more. Your weather conditions require they be buried 4' deep. Extending your home's electric in an addition will not cost nearly as much in installation or the price of copper wire. You can step into an existing bathroom easily from an addition. With an addition you won't have to go outside at all in bad weather.
Now, how old is your home? Does it meet current building code? Sometimes when remodeling (adding on to) a home it is necessary to completely rewire or replumb the home because the existing does not meet current codes and you can't just add on to what's there. This would definitely apply in a home older than about 40-60 years that has not been updated already. A lot to consider.
The cheapest option: Have hub install a dumb waiter from the garage to the studio so you can empty your hands before you climb those stairs.