1stperson view seems to use Standard Type (Character-based) Movement settings on controller, even if you picked Legacy Type. Meaning you always face the direction you look, forcing your character to stand up, as it cant face a direction while sitting. On keyboard it will be always Legacy Type in 1st person view, no matter what you pick in the setting.

I am not aware of any setting that influences that behavior to change. It could be a bug or easily moved to "working as intended" if they don't care about it, as it is not so gamebreaking.

Only thing you could do temporary is to use first person on controller, and then keybind arrow keys on keyboard to move camera left/right. Then you dont have to switch completely.