Edit: maybe download the image mentioned below, and read the bold parts first / only.
I do not claim to understand color calibration.
If you set color calibration to D50 (same as pipeline), it does not change white balance (disabling/enabling the module makes little difference, maybe gamut compression). Since the white balance module is set to the D65 reference (~6500 K), this (no adaptation, staying at D50) means the effective (scene) temperature remains 6500 K (as set by the white balance module).
It is my impression that the temperature shown in color calibration is not the CCT of the scene illuminant. Rather, it’s some kind of ‘tweak’ that needs to be applied to bring the colours coming from the D65 reference WB coefficients really into the D50 of the pipeline. That is, if the scene was really illuminated with something close to 6500K, CC would show something close to 5000 K (as no change is needed, the original 6500 K white point was already successfully remapped to 5000 K by the WB module alone).
Example:
- taking the raw from https://www.imaging-resource.com/PRODS/sony-a7r-iv/A7R4OUTBAP0.ARW.HTM
- and reading their explanation at https://www.imaging-resource.com/ARTS/TESTS/SUNSOURCE2.HTM (which mentions a colorimeter reading of 5,050 - 5,100)
- darktable’s white balance module reports an as-shot reading of 5216 K
- picking the WB from the grey card I got 5341 K
- after switching white balance to camera reference (D65):
- color calibration gives an as shot CCT of 4216 K;
- picking from the grey card in color calibration switches to custom; forcing it back to D, I get a reading of 4321 K.
I believe those 4200-4300 K values are to compensate for the fact that the camera reference D65 was too cool/bluish (too high a temperature). Applying the D65 reference WB + the input colour profile would have taken neutral/white, if the scene had been illuminated by D65, to D50 (lowering its colour temperature), so it took the real white/neutral 5200-5300K (see WB readings above) to 4321 K, which then color calibration now brings back to D50.
In other words, I believe that 4216/4321 K do not correspond to the scene illuminant, but rather where the D65->D50 (6500 K → 5000 K) transformation mapped that illuminant (estimated by the camera / WB colour picker as 5216/5341 K).
6500 K → 5000 K
5341 K → 4321 K
5216 K → 4216 K
This may well be bollocks. I just ignore the numbers in my processing, BTW. 