Excuse me if this is a sort of dumb question or if it has been asked before but; when during a run on a new profile I reach a section where I get into a new chapter, can I quit to the menu and load into the newly unlocked chapter(same profile) to skip further into the section?

For example chapter 4, upon reaching chica's bakery if you do the mentioned method you can skip doing the 3(if I remember correctly) charging mini-games and small vent crawl. There is another skip that gets past the whole chica bakery section, but that would also be skipping collectibles for the 100% run.

If you can do it, in which categories can you do so? I also imagine that (if such a skip is allowed)

We would need to see video of these to determine if and where it would be allowed. But versions of this already exist and used in runs, like right on the first ladder of the game, the autosave hits right when you climb the ladder. Quit and reload and you skip the first cutscene

I'm wondering because some skips, like the one with the ladder you mentioned, take use of autosaves. Here is the video of the skip I'm referring to, it more so takes use of a whole chapter load instead of a save file.

Near the end of the clip, I go out of bounds to the vent to reach an autosave so that my progress on collectibles and the sign bots is saved before loading the chapter. This would be for skipping doing the three puzzle mini-game thingies, the small chica cutscene and the vent crawl.

Yes, that will be allowed in runs. Really nice find