Can I ask why you want to use buttons to control movement rather than an analog stick? Buttons mean you'll get binary deflection; you're either at zero movement or full movement with no in between. I recommend setting up a 3-axis analog stick (I used this one: https://smile.amazon.com/gp/product/B07CVCSB5G/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1 )

If you want to use buttons, the easier way to do it is to emulate a keyboard with an Arduino board that is capable of using the Keyboard.h library. I used a Leonardo board in conjunction with my Mega for the game controls that Kerbal Simpit doesn't support (e.g., Map, Time Warp, Pause, etc).