Use WebExtension API instead of chrome

Created by: felixfbecker

WebExtensions is a spec for cross-browser extensions. It is implemented by Firefox and Edge, but not by Chrome, but there is a polyfill maintained by Mozilla. The API is better than chrome because it supports Promises instead of callbacks. Firefox also supports the chrome global, but only with callbacks. We should switch to using the browser global instead.

https://developer.mozilla.org/en-US/docs/Mozilla/Add-ons/WebExtensions/API