AirPods not used as output when calling from MacOS

Actually, I just realized that I was being stupid. It was just a matter of setting in FaceTime. Select "Video" and there is the subtitle "Output", where this can be selected. My settings was "MacBook Air Speakers". After changing it to "AirPods" everything works fine.

Now I realized that this might not be an AirPods issue since the same is happening when I use external headphones connected through the 3.5mm headphone jack.

Yes, this is correct. When I start a FaceTime call using my AirPods on my Mac, I do not hear the ringing sound in my AirPods, in fact, I do not hear it at all. In the top left bar AirPods are selected as sound output. Then I switch to "MacBook Air Speakers" and I start to hear the ringing sound from the speakers. Then I switch back to AirPods and I start to hear the ringing sound in the AirPods correctly. My issue is that I have to do this switching.

I tried your suggestions, but I am not sure whether I am doing it correctly because nothing seems to be different. But I am really not sure whether I am doing it correctly.