The December Solstice represents an event when there are two types of noon and two types of midnight within the same 24 hour day.

Within the Polar day at the North and South Poles, there is only one sunrise and sunset on the Equinoxes and only one noon midnight on the Solstices. In terms of Polar noon, this is when the South Pole has turned midway to the planet's circle of illumination and the maximum circumference (Antarctic circle) is reached where the are that the Sun is constantly in view is at its greatest -

https://epic.gsfc.nasa.gov/

After the Solstice this circumference begins to shrink so astronomically, in contrast to timekeeping, the appearance (sunrise) and disappearance (sunset) of the Sun as a function of daily rotation must be symmetrical.

The great neolithic alignments centred on the Solstices where sunlight enters a central chamber a number of days before and after the Solstices require the principle that the smallest declination of the Sun happens on the December Solstices otherwise the alignments would not work -

https://en.wikipedia.org/wiki/Newgrange

https://sketchfab.com/models/4d6e7d5...e8d4c51313d9bf


The answer is therefore the earlier/later sunrise around the Solstices is some timekeeping mistake but astronomically it doesn't work. These great human treasures built 5200 years ago to mark an astronomical and terrestrial event also demonstrate why axial precession is a flawed notion insofar as the North and South Poles turn annually as a function of orbital motion.