You can easily try it yourself. If GSX is installed SHIFT+P and SHIFT+J does not work anymore.
I tried both sims, and there are no problems in either. However, I think there must something going on here because, you say Shift+P is supposed to call the GPU and Shift+J the Jetway. As far as I know, Shift+P in MSFS 2020 calls the default Pushback, and Alt-P in MSFS 2024 does the same.
I tried both in MSFS 2020 and 2024, and they both works even if GSX is installed, and they call the default Pushback.
I don't think it's even possible to assign a key to the GPU or the Jetway in MSFS 2020 or 2024. Sure, the event exists, so if you trigger a >K:TOGGLE_JETWAY command, it will work, but I don't think you can assign it to an hotkey. Could be you were running some other add-on which has added these features ?
The other possibility for us in the EFB (if GSX is installed) is to use GSX commandlines or variables to attach the GSX GPU and Jetway. Is something like this available? Thanks!
Check the \Addon Manager\couatl\GSX\SDK folder, it has documentation and code sample to do Remote Control: you can command GSX to do anything the user could have done, with the menu closed, and the ability to replicate the GSX menus in an airplane gauge.