Last picture has what you need. Plug X and Y instead of break 2d vector. So basically: sign(Asin(Y))*acos(X), or something like that, you need to experiment with printing out result. That will depend on your positive and negative values you gave to axis event.
Also one thing you should be aware of: if sign(asin(Y) is zero it will zero result of formula, so when exactly horizontal (or vertical) you will have wrong results. To remedy this when sign is 0 give it 1 or -1 instead.
Just experiment with this formula, each case needs a bit different angle. It is better to calculate it here the way its easiest to use in game, than tweak it to right values all over the code.
Ps. you an always make your pad into 3d vector (x,y,0), normalize it, and do dot product with for eg. (1,0,0). You will get kind of cosinus value or how parallel both vectors are. And you can do this same with (0,1,0) so you get values for horizontal and vertical. Then you can use those values to scale x and y velocity of projectile etc. I used this for my boid math, its faster in 3d, very nice to scale turn forces or forces for projectile etc.
You can also turn your vector into 3d, and use “look at direction” node from 3d vector math. To debug those vectors use “trace” for drawing vector feedback.