I want to make my editor as cleaner as possible. Is there a way to hide the scrollbars if I'm not hovering their section? (e.g. hide the project files scrollbars if I'm hovering the code).
Short answer: No
Longer answer: The scrollbar in PHPStorm is bespoke as you can see with code highlighting and on hover effects. It's not controlled by the OS. So the only way to change it would be via PHPStorm options which don't exist. But you could file a request for it.