Improve code as a result of
https://gitlab.com/gitlab-org/gitlab/-/issues/288339

This commit:

- Fixes `service_desk_root.vue` `incomingEmail` prop from being mutated
- Removes data properties in the Vue root component
- Converts root component props to provide/inject
- Removes an event hub in favour of component events
- Removes service class
- Completely overhauls the related tests