After I set the GIMP image preferences to 32bit floating point en using Linear Light, I created a new image. Then I set the foreground colour to R=50%, G=50% en B=50% and fill a rectangle with this foreground colour. To my surprise the Colour Picker tool now shows RGB values of 0.2140 instead of 0.5000 as I would expect because I am using linear colour. 50% is 50%. Since 0.2140 is the linear colour equivalent of 0.5 in the perceptual gamma space, it seems that GIMP treated my colour setting as a perceptual gamma number and converted it to linear light. Really strange. Why does the program think I started with Linear Light in the first place?
AFAIK the color picker doesn't display the values, you must be talking about the pointer tool display (Edit: I stand corrected)
When you set the color to RGB(.5,.5,.5) these are gamma-corrected values. "Linear-light" is about internal values and processing.
In the color picker and the pointer tool, there are various display options. The
Pixel one shows the internal values (ie, RGB(0.2122,0.2122,0.2122) for the middle-gray)., the others are gamma-corrected when it makes sense (RGB(0..255), RGB(%), HSV).
Another place where you have the choice between linear and gamma-corrected values is the histogram.