iMovie Audio Video sync problem

Hello, I have recorded a film using iPhone 13 Pro Max and Shure Motive Video app through a stereo interface (Focusrite Saffire 6 USB 2.0). The film plays in sync when played back in the app on the iPhone.

When exported to my iMac (MacOS 15.3.1) per airdrop from the Shure Motive app, it loses its sync (the video is quite behind the audio) and plays almost one full tone higher than the original.

When I put it into iMovie, it plays again at the right speed (pitch). When I sync it with the processed audio file gained from the same recording, which then I put under the film, it both audios play in sync (within reasonable differences), but when I export it from iMovie, the film is again behind the audio and almost full step too high in pitch. This is also true when I export it out of the iMovie with its own original sound track, which plays in sync within iMovie, but not, when exported. Export method doesn't seem to change anything, whether it is for social media or just export.

Thanks for suggestions!