Transmission will not go into reverse

I have a 2004 Chrysler Sebring with a 2.4L dohc and automatic transmission with 115k miles. I recently had the timing belt and water pump replaced. Shop left the front 2 engine mounting bolts off and the rear one loose. Picked up car after business hours drove it that evening and kept hearing a strange metallic squeak.Returned it to the shop the next morning and as i was driving it began to smoke and stall with the temp gauge pegged. They had also left a hose to the heater core disconnected. Could the engine not being mounted to the chassis and/ or the overheating have damaged the transmission.

also the trans fluid and screen were changed at 90k. Checked the fluid level it was fine and the fluid was not discolored

Those guys clearly aren’t the sharpest knives in the drawer so it is anyone’s guess what they did or didn’t do but here’s the first stab in the dark:
Since they clearly messed with your radiator, maybe they kinked one of the ATF cooling lines so it wasn’t being cooled properly?

“They had also left a hose to the heater core disconnected.” The transmission is only one of the issues you need to discuss with the shop. It is likely you have engine damage as well. It is time to have a serious conversation with the shop’s management about what they are going to do to repair the damage caused by their negligence.