The typical police cruiser has a much more severe space premium, particularly for first aid supplies. An ambulance is a whole box full of first aid supplies.
It’s about the size of a hand drill and can probably be miniaturized further, heck you might not even need to inflate with an electric pump, you can probably have a small electronically controlled valve and a CO2 canister similar to those used for quickly inflating bike tires.
The only real issue I see with this is it’s actual applicability most stab victims get stabbed multiple times, often in the same area plugging one hole might not do you good when there are 5 more around it, heck the balloon might exacerbate the bleeding from adjacent injuries.