Colourize 3D graph with 2D equivalent of F(z)

Do you mean a Gizmo plot with 3D scatter plot (I am not sure since you just appended a 2D scatter plot)? Gizmo's can be colored in an arbitrary way by using color waves. See here:

In your case you would need to create a N x 4 dimensional wave (N is the number of triplet points) and fill in the desired RGBA values for each triplet point (in a range from 0 to 1; use 1 for the alpha value throughout if you don't want transparency) . If you need something similar to f(z), you can write a simple script to extract the z value from your data and then assign the desired color to the color wave depending on this z value. It is a bit more involved than for 2D plots, but the benefit is that you can literally give every point a precisely specified color, i.e., it is much more general.

Chozo is absolutely correct.  I would just add a shortcut that you can use ModifyGizmo with makeColorWave={...} to get behavior similar to color as f(z).