GSX therefore did not fully handle the pushback, so I could not taxi to the runway.
I had to restart GSX Couatl engine to get rid of the GSX blockage.
Please clarify what do you mean with "blockage".
Because, if you mean the airplane was frozen, it's not consistent with your report, since the only thing that could have caused the menu going back to default without the pushback completed, was an automatic restart of the couatl engine performed by the auto-restarter which detected either an error or a simconnect timeout, so it did its job to restart it automatically, resulting in the previous pushback state being reset and the menu going back to default when outside a parking.
However, a restart would also have unfrozen the airplane ( if this is what you mean with "blockage" ), exactly like when you restarted it again, manually.