I finally found the bug report which I thought was related:
https://github.com/geany/geany/issues/1428
There's a window with one tab with Geany editor and one with the Preferences window created by Mac OS. And in this bug report I think there's just the editor tab displayed by Mac OS for some reason.
(And the Mac OS expert in the bug report wasn't @codebrainz but @elextr ;-)
@codebrainz The problem is that it involves Objective-C which we don't use in the code at the moment and from what I remember Colomban wasn't very keen of using it (which then complicates build settings and requires linking objective-c runtime).
@nimdanor Yeah, I suspected that, I think it's really a tab. Isn't it possible to close it? There might appear a close button when you move the mouse to the left of the second "title bar".