Ok so, why is, new game's rules are "use a saved file", when Any% is "Start a Fresh New Game"? Or this could be a Glitch on Speedrun.com...

New Game + means that you can use a full save file. Any% might be better called "Any% NG", it's starting from a fresh file.

The distinction any% is making is really in contrast with 100%, where you have to buy every upgrade in addition to defeating the boss.