"I was initially hoping to get some insight on e.g. which pairs of squares had the fewest moves for a given piece etc." This may not be quite what you were ask

"I was initially hoping to get some insight on e.g. which pairs of squares had the fewest moves for a given piece etc." This may not be quite what you were asking for, but it's close, and has the advantage that I can link it right now. Tom7's Elo World chess video has where pieces start and end up, and their survival rates, as a chart: https://youtu.be/DpXy041BIlA?si=Zdh6Rh6mekatp2-q&t=815 https://youtu.be/DpXy041BIlA?si=Zdh6Rh6mekatp2-q&t=815