feat: call migration and wait till its done before calling browser storage

Created by: ijsnow

Migrations in the browser extension weren't completing before other calls to browser storage. This means that things can fail when the browser extension storage gets in a weird state (example). This PR makes sure migrations are called before any other calls to the API are.

This PR is based on bext/options-menu to make it easier to merge that PR since it should be merged soon after this.