I know this isn’t darktable, but I think teasing out the operations has merit…
First, this is “as-shot” white balance:
It’s really not bad, just a little warm if you pixel-peep the white feathers. So, I took a patch from the bottom bird’s white-est feathers:
Truly white feathers and a more interesting sky color, with a slight adjustment like this (multipliers generated from the patch):
whitebalance:0.858,1.000,1.200