If you write and read to "user://" in Godot, it'll automatically work with browser storage on browser exports without doing anything special. Tho when I'm just doing web dev and I need to save something small, I just use localStorage which you can look into.
I think you should be able to, you can definitely make browserStorage directories normally in web dev.
I haven't watched any videos, I just noticed writing and reading to/from "user://" works by happenstance :) But if you read the Godot docs on saving, all of that should apply.
