[pkscout]

Dunno if my impression is correct, hope anyway I explained the issue.

Your impression is correct.  That audio profile change is triggered when Kodi sends an OnPlaybackStarted event.  I don't know why Kodi isn't sending that event when you start playback in your use case, but that's the issue you need to figure out.  There is no work around on the audio profile side for that.

I know is a lot to ask here, since it's not an add on issue, but I have no idea on how to investigate it further (which is not really a deal breaker, just... strange ), can you suggest something (i.e. which log to collect etc)?

If you turn debug logging on in Kodi and then duplicate the issue, that's the best way to gather info for troubleshooting.  I'd probably also include the hardware info for your Kodi machine as well as that audio device.  Find the right place in the forum (likely one of the OS specific areas), create a new post, include all that, and maybe someone can help.