Even though the key is broken off inside, which negates putting another key in or picking the lock, is there any chance you could insert the broken end of the key until it touches the end of the broken key, then ever so gently try to turn it while tapping and pushing in and out on the cargo door? The idea is to relieve the pressure on the lock tab inside.
I know on mine that the fit isn't the best, and the locking tab inside is tight against the frame. Putting pressure on the door could relieve it enough to turn.
Another thought, by any slim chance is there access from inside? My last TT had a lift up panel under the bed to access the storage. I could reach the storage bay door from the inside. If so, you could remove the nut on the back of the lock cylinder, and let the tab fall off.
Do both sides of the compartment lock? A lot have a thumbs latch on one side and a lock on the other. Your pic is too dark to tell. If you can open one side, pull the door open enough to get your arm in there, maybe you could work the nut off the latch tab on the inside. Or maybe get something in there to try to jockey it open. There is some flex in the doors, they will bend a little without damage.
Is it a pass through compartment with a door on the other end? If so open the other door, pull stuff out and crawl in to take the thing apart from the inside.
Or a drill and bits. Drill out the cylinder until it comes apart. New ones are cheap enough. Should be able to do that without damaging anything.