Display the same color as picked
Blender's default view transform is set at Filmic. Filmic is useful when you have brightness more than 1.0 in RGB. For NPR this will make the viewport displaying a more desaturated color.
To display the same color as picked from the color selector, make sure the view transform is set to Standard.
Recursive color picking while in Filmic view transform will cause color divergent
Doing recursive color picking when texture painting in Blender while in Filmic view transform will cause color to diverge extremely from the initial picked color. Therefore only texture paint in Standard view transform. All color manipulation in the shader editor and the compositor will also behave unpredictably.