Sadly there is no international air vest certification standard. So there is no way to know how well the air vest will protect you.
The French have come up with their own standard (NF certification (S72-800:2021)) and some of the French air vest companies are starting to get certified under it.
For the past 4 years, I have ridden in a Point Two hunter. I don’t do cross country so I don’t have to wear a hard shell underneath. I agree that adding an airvest over a hard shell will not change how hot the hard shell will be.
Since you are eventing, there are fewer options to choose from. Most of the new vests (Horse Pilot, Freejump, Seaver) are aimed at the jumper world and are meant to be worn by themselves.
The original companies making air vests (Point Two, HitAir, Helite) started off in the eventing world so their vests are made to be worn over a hard shell.
I would also recommend that you find a company that will service their air vest. Since it is a mechanical device you want to make sure that it is checked regularly. One of the big reason I went with Point Two is that they do service their vests, so I know that the manufacturer has checked it and it is in a perfect operational state. In addition they have offices in the USofA so I can have my vest serviced quickly.
Good luck and let us know what you decide on.