Very nice job on the lighting!

get rid of black background and neutral grey

Flattish; this suffers from "compartmentalized color", the common case of filling the areas of a painting with flat colors and then applying black and white to make "light" and "shadow". In drawing with limited color, you can use that as long as there's a color composition overall. But in a painting, it's a serious flaw. Well, in 99.9% anyway, since El Graeco somehow had been getting away with smearing pure white to make highlights without making it look disgusting. (Under a painting, I mean the work which uses color to create an illusion of lit environment, not for purely emotional, represenative or other purposes; the medium can be any.)
What to do to avoid it - well, first of all, follow the classic rule of "tone first, color second": the flawed coloring does exactly the opposite. Plan the color composition so all colors form a harmony. And think of how the colors interact: how presence of a colored object affects other color objects in the painting. The latter is a skill learned slowly, I have to admit, but it's a very advantageous one to have.
A good starting point / refresher is the section on color in "Creative Illustration" by Andrew Loomis. And of course, nothing beats exercising the eye by observation and identifying tone and dominant hue in everything.