Solstice has nothing to do with the orbit of the sun or proximity to the sun.

It is about the angle of the earth relative to the sun. The earth leans a bit. For half the year, the southern hemisphere faces the sun more directly, the other half the northern hemisphere faces it more directly.

Summer/winter Solstice marks when the lean is most head on/most leaning away to the sun for each hemisphere.

This happens on the same day each year because the lean is constant.