I have been facing the same issue on my Xbox Series X, and I may have found a fix (or at least worked for me). Would like to thank @TyingTunic30431 for mentioning:
I am facing the same issue on XBOX Series S, and it could be reproduced also on PC when XBOX gamepad is connected to PC via Bluetooth.
This game me an idea, I started the game on Xbox with my controller disconnected from the Xbox (was connected to my pc but turning off the controller works), and had a keyboard and mouse connected. With that, the game starts and runs fine, so it seems like an issue with the controller in some way. When on the main menu and I connected my controller, it crashed straight away.
I then delated all of the control profiles for the mouse and the keyboard, so the only profiles left were the default built in ones (which you can’t delate), this is doing using the preset manager on the controls screen (button is at the bottom next to “go back”). I also cleared and disabled the rolling cache, but unsure if that was actually needed.
Then did a quick flight with a different plane to force it to sync (unsure if needed) (also using a different plane allows you to check if it did as when you next go to world map it uses the plane you used last), before clicking on my profile in the top right corner to sign out (again, probably not needed but I wanted to make sure it synced).
I then quit the game, started it on cloud gaming on my pc (since that does work), and did the same again, clearing the controller presets/profiles, quick flight to ensure it syncs, signing out, etc.
After that, I started it again on my Xbox with only keyboard, after loading into main menu, I connected my controller, it did not crash and it all worked, flying etc. I then restarted the game to verify, and with controller connected it did not crash. So this has seemed to have fixed the issue for me (or at least for now).
Based on that, seems like to me the problem is the controller profiles are getting corrupted? But that doesn’t explain why cloud gaming still works, and I never had an Xbox controller plugged in while playing on PC.