I 'm looking for information about the time when the air 3 can fly (without any problem) in once.
I will explain the question : it is not about the time with one battery, but in the case i change the battery and the drone can fly like "continuous" (after a short landing and takeoff)
is there some restriction or some stress test like after X changing of battery, does DJI recommand to stop the fly ? or a message appear after x minutes of fly.
Regards

I have used it for 6 charges, like 3 continuous hours, with small 2-3 minutes for changing batteries....No issue, but rotors were very hot at the end. No messages, all fine, except the bugs that was already sent to DJI for solving....
I do not know if works more, depends also of how hot is outside...My flight was at 16 degrees Celsius, probably at 30 degrees Celsius will appear Overheating messages.

I’ve ran DJI Waypoints missions with my Air 3 and went through 2 plus batteries in about 75° to 80° F temperature and had no issues. About 30 minutes on one battery and I believe about 28 on the next one. The third battery probably had about  15 minutes of time while flying manually and not one issue. I also have a MA2 which Ive had since August 2020 with about 100 hours of flight. I have 6 batteries for the MA2 and I’ve flown Dronelink missions with several continuous battery swaps on missions. I’ve also have switched to the DJI Fly and in the end I went through all the 6 batteries. I get roughly about 20 minutes or a bit more with each battery and never had any problem. I’ve ran through most of them many times and no issues. That’s at least 2 hours of continuous flight time. The temperatures are generally between 90 to about 95° F during the summer and I’ve never had any issue with gimbal overload, over heating or any ESC errors. As mentioned by GEO_Drone the most important thing is the actual air temperature which can affect the drone or battery temp. I’ve had one flight Airdata reported with the highest battery temperature at 140° but that was in Tucson Arizona at 108° with very high humidity. Some flights at roughly 126 to 130° or so in about 95° F but most are not higher then 120 and lower. So it’s not how many batteries you go through or the total flight time, it’s the air temperature which could be an issue if it is really hot. Even then I haven’t had an issue flying in 95° to that one at 108°. So if not in a high temperature environment you could go through as many battery as you want. As always anything is possible and there may be a few pilots which had issues but I’ve haven’t read an aircraft not starting up due to overheating or shutting off mid-flight. There is no message after any amount of flight time and I’m sure DJI will say you should always let the drone cool down for a bit before running another battery. Of course that’s so if anyone did have an issue they would say to follow their recommendations. Enjoy.

You can fly all day long without any worry.
The drone cools itself as it's flying.

Hello, there. Thank you for reaching out. To confirm, please know that the DJI Air3 doesn't support battery hot swapping. However, when one battery is depleted, you can quickly swap it out for a fresh one to minimize the downtime of your flight. Please be cautious with your flight environment to avoid inconvenience. Thank you for your support.