If you use modern color flow in darktable - don’t save white balance preset, but save color calibration preset and leave white balance alone.
Technical explaination:
White balance ‘as shot’ is nothing more but a set of coefficients for channel multiplication to get the “ooc” white balance calculated from image data. the “as shot” is not much as setting but more of detection if the coeffs set are actually “as shot”. So if you copy “as shot” you’re not copying “as shot” setting, but copying coefficients… And when you paste it on another image with different coeffs calculated then it’s no longer “as shot”
Color calibration on the other hand CAN copy “as shot” setting (which works a bit different).