I changed the days in nursery and applied it: why did my field planting date not move?

On purpose, so your bed plan stays intact: your field planting date is what your beds and your Crop Map are planned around. Heirloom moves the Nursery start date instead, earlier or later by the change in days.

The first harvest follows the new days to maturity, and the plantings of a succession follow too. If you want the field date itself to move, change it in the planting window.

The steps are in Update the plantings already in your plan.