Shader nodes do not communicate back to Geometry nodes. You’ll need to input the hue value to geonodes, output it as Attribute, then read the attribute from the shader
In the exact order you’ve described (read a value used by shader in Geometry Nodes) - you can’t. But I fail to understand why you’d need that, since you can either use Driver to sync some value between Geometry Nodes and a shader, or do it as in my 1st post (first, write a geonode parameter into attribute, then access it through shader)
BTW, in your example, the shader processes a Vector input as RGB color model, not HSV. Try using Hue-Saturation node instead