I have not consciously activated Shft/Ctr F12 in another application
You are not controlling this, it's the application own code that asks for a key and, whoever gets it first, will block it from reaching other apps ( but this is also depending if the other application asks for it in exclusive mode or not )
I have even tried reinstalling P3dV5.3 but this did not change anything.
Of course. If the other app that took the key is still active ( which will be, if it has an add-on.xml in the Documents folder, which doesn't go away just because you reinstalled the sim )
Are you able to open other GSX menus, from the GSX own menu, instead of using the keys ?