We went to MK Jan 1, 2024 and it was not too crowded, particularly in the morning. I think it so many people go to MK on the 31st that it is not too crowded on the 1st.
Oops misread your post. Yes we were at HS on New Year’s Day 2023 and the crowds had considerably thinned out (you could walk up to Fantasmic 15 mins before and still get a seat).