Mazda Repair Questions? Ask Mechanics for Answers ASAP
I don't know whether you had the door replaced as part of an insurance claim or as a cash customer, so I'll try to address both scenarios:
Insurance Claim - contact your insurance representative and let them handle the situation - that's what you pay for.
Cash customer - tell the body shop the car came in without that issue. Since it happened while the vehicle was under their care, they are responsible for anything that's a direct result of their work. They need to either get that done or refund your money so you can use those funds to get the vehicle repaired correctly somewhere else.
For this door replacement to be done correctly, the procedure calls for the battery to be disconnected and all the wiring, switches and actuators transferred to the new door before reconnecting the battery - as it is, it looks like they missed a step somewhere in the procedure.