I only heard about issues in Ubuntu. Did you check also global Console (Ctrl + Shift + J)?

Are you looking at the extension's console (about:debugging > This Firefox > Extensions > Inspect > Console)?

@TyDraniu: thanks for your reply. You are right - indeed the output shows up in the browser console. What confused me is that in my case it can take over a minute until the message emitted by the native app shows up in the browser console. I can see that from the timestamps in browser console and timestamps that are part of the native app log output. Or may be it depends on the amount of data produced by the native app - i.e. it shows in the browser console only after the native app produces enough output to fill some buffer ...

@zeroknight - in fact that is another thing - I expected the native app output to show up next to the background script log messages (i.e. in about:debugging ->Inspect->console, but that is not the case.

Either way, the answer to my question is: "Yes, it is supposed to work. And it does". And I have to deal with the details on my side. Thanks to both of you.