So I have always heard to wait till prestige turns to start to search for recruits for my watch list.. I have on all three of my teams for multiple seasons done a search right after recruit generation during the year and after the prestige changes. For the same Div as the team I see zero difference in the top players that show on the search. So I see no reason not to start searching early. Am I missing something?

No idea if the list changes as your prestige changes.  I would assume it would as well.  But either way, it shouldn't really matter since I assume you are FSS'ing most if not all of the players you go after, and it makes the most sense to wait until the world rolls over and you have all of your recruiting money to scout, so that you have the money to scout all the states you want at once to get the full discount.