The Pushback is not stuck.
You are using the FS Labs A321, and FS Labs has sent a command to GSX to suppress all its text messages, likely because it's supposed to control GSX by itself ( opening and closing doors automatically ), so you think GSX is stuck, but it's not, it's just that is waiting for you to fix some something that is preventing the pushback, like closing a door, removing the service vehicle, wheel chocks, etc, but since FS Labs has suppressed all the text from GSX, you don't know GSX is waiting for you to do something, and you think it's stuck, but it's not.
Also, I believe the FS Labs should be able to close doors and remove other constraints automatically, but it might not do it if you don't use the correct procedure from the ATSU menu ( I don't know exactly how it's done, please look for some tutorials or ask FS Labs ), and might intentionally add some extra delays compared to the standard GSX, which is also why they suppressed the messages, so you won't be constantly nagged because the airplane is waiting to do something else.
