Refactor the CSS rules for the overlayContainer

This PR refactors the CSS for the `overlayContainer`, to achieve the following goals
* Reduce unnecessary duplication of CSS rules.
* Remove the dependency on `doorHanger`, since using that class seems out of place here.
* Serve as a prerequisite to a follow-up PR I'm working on, that will change how we interact with the overlay, since the current way of doing this won't scale well if we want to add more overlays (e.g. #3985).

/cc @timvandermeij Would you mind reviewing this?