I checked this and yes, I can only replicate it with the Fenix A320, doesn't happen with the default Asobo A320, the FBW A320 or the PMDG 737.
What is really happening, is that for some reason, when the Fenix is loaded, when GSX contacts WASM to set some variables to notify 3rd party airplanes it operated the stairs, in case they need that info to do something, and at that time, the WASM stop the connection with the sim for some reason, and this will confuse the whole menu, because it needs to rely on it to work.
With other airplanes, operating the stairs just operate the stairs and, opening the GSX menu, doesn't trigger anything.
I assumed this might be a general WASM issue in the sim, like a conflict between modules but, when I tried the PMDG 737-800, which also uses WASM extensively, but the same issue doesn't happen, so it seems to be something specific with the Fenix, we'll report to them when we'll discuss about integration, since that's not the only thing that will have to addressed to have everything fully working.
In the meantime, just don't use the Operate stairs with the Fenix A320, until we'll know more.