I would like to ask if there could be possible in GSX windows place a small perhaps icon or text just to inform if pushback is available or not
It's already there: just open the "Customize this parking" position from the GSX menu, to check the Pushback for your current parking or, if you are not parked yet, use the "Customize Airport positions" from the "Couatl powered products" menu. You don't have to do any edits, just check the Pushback availability and, eventually, edit to suit your needs.