I am still asking myself if this is a "me" problem or a SU4 Beta problem with GSX
It's an SU4 Beta problem. Not a problem "with GSX".
So it might be godd to prepare GSX than, if those issues are coming from the Sim.
There's not much to prepare here, we can't do anything about MSFS own bugs, other than reporting them.
So why is GSX giving me a third stairs with even none making sense handler texture on it.
You are assuming GSX is doing that, because that stair "looks like GSX", but it's not. What you see there is a default ground vehicle handled by MSFS, which HAPPENS to look like GSX, because GSX replaced its visual model, but it's still an MSFS own ground vehicle handled by MSFS, that also explains why the operator is not the one selected by GSX, because that stair there is NOT called by GSX.
The bug in the sim here might just be it decided to send a stair on a service door for no reason, same as when it docks a jetway on a rear door or a service door, if you parked in a position that would make those doors solvable.