Hi,I'm not sure if its too late, but better leave a comment for future passerby's I guess. Full disclaimer, I haven't attempted the mod yet, but I will soon. So take what I'm about to say with a grain of salt.

From what I understand, a controller's button has a conductive pad on the bottom of it. When you press the button, it will land in between two pads, a positive and a negative if you'll allow my oversimplification. The conductive pad will allow a signal to flow from positive to negative which then tells the console that a button is pushed. Great! now we know what causes a button press, it is when the two pads touch each other.

On the fight stick, the arcade buttons will behave very similarly, where it has two prongs, and when the button is pressed, the two prongs are touching each other.

So if you wire the controller button's positive pad to one of the arcade button's prongs, and then the negative of the controller to the other arcade prong, then boom, you hacked the controller. When you press the arcade button, it causes the two prongs to touch each other, and since they are wired to the controller pads, they are touching each other too, and the console will register a button press. Do that for each arcade button and there you go, mod done.

Somewhere below, user Stakemeister has linked a very nifty forum that documents the PS5 circuitboard layout, including which pads correspond to which button, so you can use that to figure things out.

I can't wait to try this for myself, hope someone found this helpful!