At the end of the previous post, I suggested an alternative was to select a lighter region of the sky and darken it. Here are the details.
The strongest effect of circular polarizer is at an angle of 90 degrees to the sun. But when shooting with a wide-angle lens the field of view encompasses an area beyond 90 degrees (and less). This can result in uneven exposure and saturation across a blue sky.
In this case I would like to use Lightroom local adjustment to fix the right side of the sky.
Do not try to completely match the areas, rather aim to reduce the impact of the polarizer.
Now I turned on both adjustments, one to lighten the dark patch and the other to darken the right side. Spend a little time tweaking the amount of each adjustment. But not too much time, you are not aiming for perfection, just mitigation.
Finally, in the field one could adjust the polarizer to move or lessen the darkening and avoid all of this fussing about.