Well, I have the time and really want to fix all the issues of my kids 2011 prius. The search did not provided a case, maybe only for gen 2, about the AC cooling mostly left (driver side). On the passenger side is just blowing hot air, probably recirculating the same cabin hot air. After some minutes later, the passenger side vents started to provide cool air, maybe because it is already recirculating the cool air provided from driver side vents. I have not looked inside the area because want to see if I can find some clues of where to start looking for. No DTC related to AC, at least on the dr. prius and OBD app, and have not looked with the techstream if there is a section that could show something related to the AC. It's really hot outside, day or night here in south Texas so I prefer doing some pre-research inside before the adventure outside. Maybe it is a door not opening because some actuator not longer working... I don't know, but maybe somebody else had the same issue and already found a way to fix it.
There are a couple little motor actuator door damper moving devices connected to the air box similar to the generation 2 if they're not functioning correctly for all I know you could be letting heat into the cabin You're sure the refrigeration cycle is working so when the air is on outside under the hood the gray pipe marked l is in fact cold? If not well then that's one place to be looking and see why we're not making cold If you're making cold and it's not getting in the cabin then it's one of these blend door devices that's not opening or closing sometimes you can disconnect the little motor box put the door where you want it put a piece of tape on it and it'll sit there all summer till you get time to fool with it I didn't know the generation 3's had this problem they're certainly limited room to work that's for sure You can look on the parts breakdown of the car and see the two or three door operating devices that are on evaporator case is what that is.