Understood. That is what I tried. On the keyboard I pressed and held alt-3 while moving the stick and it has no effect.

On my saitek programming software I can simulate holding down a key (or combination of keys). However, if I can't get the key combination to work, I'll have no luck with button assignments.

In-game I've try to calibrate my flight stick (not using the saitek software at all). The only buttons that seem to register are the HAT switches and POV buttons. The other buttons (including the trigger) don't show up as a button that can be configured, however pressing the trigger button does fire weapons. In addition the next and previous buttons don't show me the additional commands.

When did you try binding keys in-game? If you tried that AFTER you've bound keyboard commands to your joystick the game obviously isn't going to recognize the buttons as joystick buttons anymore because you've set them up to be recognized as keyboard commands.

as you can use software to assign keyboard-functions, i guess there's some special driver used the game doesnt fully recognize.

whats the joystick labeled in device manager? "hid-compliant game controller" or something different like "saitek flightstick" or whatever?

maybe you can try to manually change the driver to the standard-one by microsoft

or completely uninstall any software by saitek, reboot and try again to assign buttons ingame. just for testing.