I have the exact same issue connecting wirelessly to Android Auto on my Karoq SL 1.5 2023 model.
I have had the car around 10 weeks now, I notice that on the notifications in the car that the e-sim data connection is not available, I am not sure if this is causing an issue or not but the dealer seemed to think this was the problem and Skoda are aware of it and trying to fix the issue.
It's very frustrating as I had a 2021 model and AA worked fine wirelessly.
I have a Pixel 7 pro, my wife has a Samsung Flip 5 and both phones are doing exactly the same thing. Will connect for a few seconds after starting the car and then drop out. Works fine with USB cable.
On another note I cant register myself as a primary user even with both keys. Again I'm not sure if this is the problem.
I will follow this thread in the hope we get answers to this very annoying issue.