Using the aircraft to request the Jetway, then once connected, click 'Operate Jetway'.
Doesn't make any sense. If the airplane connects the jetway on its own, doing "operate jetways" in GSX with the already connected jetway will result in the jetway disconnecting!
That's because there's no such thing as a "connect jetway" or "disconnect jetway" command in the MSFS list of SDK events, there's only a Jetway "toggle", which will invert the jetway status so, if you call it with a connected jetway, it will disconnect.
Just use "Operate Jetways" from GSX or Boarding/Deboarding, which will operate jetways automatically.
Also, looking at your screenshot again, it's clear the stairs you had there didn't have anything to do with GSX possibly being "confused" and not reading the jetway so, scratch all my previous explanations about possible conflicts, because those are NOT GSX stairs, they are PMDG ones, and PMDG doesn't know about the scenery own jetway, it will always displays its own stairs, no matter what.
Which is why, when calling Boarding/Deboaring from GSX, it won't happen immediately, because GSX will first have to operate the PMDG FMC to send away the PMDG stairs and other vehicles, so Boarding/Deboaring will start after all these vehicles are gone.