So the joystick in question is the Thrustmaster T.Flight HOTAS X. In the dosbox config i set "joysticktype = fcs".

Since this joystick has 12 buttons and a hat, the plan is to map even function to either one of the buttons or the hat. So i went to the key mapper (CTRL-F1) and mapped everything there. Every button & hat is recognized in the mapper and can be mapped without issue.
I.e.:
Increase speed "+" mapped to Button 8
Decrease speed "-" mapped to Button 9
Shield config "s" mapped to Button 10
Next target "t" mapped to Hat Up
Prev target "y" mapped to Hat Down

The buttons work perfectly fine, both in the game as well as on the command prompt (i.e. if I press Button 10, an "s" appears the command prompt)
But the hat is not recognized. So when I press hat up or down, either a "t" or a "z" should appear at the prompt, which is not the case. Needless to say, that it also doesn't work in X-Wing.

I already tried to remove all other hat mappings, which were just RL hat mapped to emulation hat. But it didn't help.
Anyone got an idea, what might be wrong?

I figured it out. It is an issue with DOSBox Staging 0.75.0. I switched from Vanilla DOSBox 0.74 to the Staging, because it has more features I like, especially a configurable deadzone for joysticks, which makes playing games with analog sticks so much better.
So in Vanilla DOSBox 0.74 is just works, no issues, can map everything and everything works like a breeze.