hmm, this is an odd behaviour... seems like some issue with background().
When i remove the background, the color seems to be right, same if i draw a white rectangle under the colorPicker.

But if the color-picker is static, you should not create it on every frame, a more performant way would be to create an image, and use that image inside draw. Would solve the described issue too. Something like this:

1. import processing.opengl.*;
   color c;
   PImage picker;
   
   void setup() {
     size(300, 300);
     colorMode(HSB, 360, 100, 100);
     picker = colorPallete(width-20, height-20);
   }
   
   void draw() {
     background(c);
   
     image(picker, 10, 10);
    
     c = get(mouseX, mouseY);
     println(hex(get(mouseX, mouseY)));
   }
   
   // creates a color-picker-image
   PImage colorPallete(int width, int height) {
     PImage img = createImage(width, height, RGB);
   
     float h, s, b;
    
     img.loadPixels();
     for (int x = 0; x < width; x++) {
       h = map(x, 0, width, 0, 360);
       for (int y = 0; y < height; y++) {
         s = map(y, 0, height, 0, 100);
         img.pixels[y*width+ x] = color(h, s, 100);
       }
     }
     img.updatePixels();
    
     return img;
   }