It seems to work after all, with an adapter....
https://youtube.com/watch

Not Osmo, of course, but Dji Action 2... ;-)

The DJI Mic consists of two transmitters and a receiver with a 3.5mm jack for connection to a camera. The DJI Osmo is an action cam without a mic input. Because the DJI MIC transmitters record independently internally, you can easily flap and sync the files in post-production.

Hi, I can't tell you that. I don't have a DJI Action. I recommend YouTube to learn more about it.