For the 12 endings/ Bucket catagory, would the start of the run be from a fresh file or once the bucket is first available.

rules state that it starts upon your first input in-game, so basically your first movement so you can set up stuff and have the bucket beforehand

First input would be from the start of the game though right? Pre-bucket? The bucket isnt immediatly unlocked. So by the rules it would be prior to collecting the bucket, then once you have the bucket finish all 12 bucket endings defined by the rules. Am I wrong?

I think by first in-game movement it means by when you begin the game again. So by that logic, you can set up the bucket before starting the run

^^

You don't have to start from a fresh file. You can do pre-setup, such as expo, but also short hallways + jump storage.