I expected that the camera module records stereo audio. In the specification I found 'Audio Output 48 kHz, AAC' - no information about mono-stereo.

When processing my first shots I realized that the mp4 contains two channels, but they are identical, the two channel has THE SAME SAMPLE so the recording is completely flat mono. Is this a software bug, or the microphone of the main module is really mono?

There's only one microphone on the camera module.  It therefore only provides mono sound.  Attach the screen module, and that adds three more mics for configurable, class-leading surround sound.  This is very clearly stated in reviews and Action 2 promotional material.

"Attach the screen module, and that adds three more mics..." - yes, THIS is clearly stated in reviews and promotion material. BUT it is not stated that the basic module only produces mono sound, not even in the official PDF manual. It is actually hidden. I also watched 8-10 independent comparison videos before purchasing, no one spotted this relevant disadvantage. I expected one basic quality stereo microphone in that buttonhole, like it is solved on the cheapest smartphones. (I know, water and dust, but this is not the cheapest smartphone.) I am very disappointed now

I don't understand why you thought one microphone was going to provide two different channels of sound.  Nobody mentioned that the sound from that one mic is mono because one mic always provides mono sound.  The manual clearly shows the layout and quantity of the microphones on the camera and on the screen module.   I'm sorry that you are disappointed but it's the laws of physics - one mic = mono sound.

Yes, I also know the law of marketing: do not write "mono" or "single channel" anywhere, because it is not state of the art. Write "one mic". Most users won't notice anything.

The nearest equivalent to the Action 2, the Insta360 Go 2, also only has one mic and mono sound.  But even worse, it has no option for connecting any means of introducing stereo sound.  So the Action 2 has a considerable advantage in this respect, as not only can the screen module be connected, but you can also connect to that almost any USB audio device for input and output.