Hissing noise after jumping dead battery

The hissing and smoke could likely have been too much pressure in the AC system and some of it vented. Look on the passenger side fender for the round receiver / drier to see if there is an oil stain near the pressure relief valve. The car can be driven if that's what it is, but the cause will need to be found. Usually it's due to a restriction in one of the hoses, or someone was recharging the system and over-charged it with too much refrigerant. That should not be related to the dead battery.

Does the AC seem to work properly? If so, that hissing might not have been refrigerant venting. Perhaps the serpentine belt was slipping and smoking. That slipping can sound like a hiss.

I think the place to start is with the draining battery. There has to be quite a draw on it to go dead overnight. Testing for that draw has become very complicated in the last 10 -15 years because of all of the computers on the cars. Some of them take up to 20 minutes to go to "sleep" mode after stopping the engine. During that time they can draw over three amps. If something prevents a computer from going to sleep it will continue to draw that high current until the battery is dead. That could be in as little as four to six hours.

Your mechanic will have to set the car up to be ready to make measurements after the computers have gone to sleep. That is complicated by the fact that nothing can be disconnected from the battery, otherwise the time-out process will start all over again.