Improve service desk settings frontend code

What does this MR do?

In #288339 (closed), an issue was raised where a prop of service_desk_root.vue is being mutated. Initially, this MR was going to fix only this but other improvements were spotted which are also included in this MR.

This MR:

• Fixes service_desk_root.vue incomingEmail prop from being mutated
• Removes data properties in the Vue root component (why were they there??)
• Converts root component props to provide/inject
• Removes an event hub in favour of component events
• Removes Service class
• Completely overhauls the related tests

Screenshots (strongly suggested)

No visual changes.

Does this MR meet the acceptance criteria?

Conformity

• Changelog entry
• Documentation (if required)
• Code review guidelines
• Merge request performance guidelines
• Style guides
• Database guides
• Separation of EE specific content

Availability and Testing

• Review and add/update tests for this feature/bug. Consider all test levels. See the Test Planning Process.
• Tested in all supported browsers
• Informed Infrastructure department of a default or new setting change, if applicable per definition of done

Security

If this MR contains changes to processing or storing of credentials or tokens, authorization and authentication methods and other items described in the security review guidelines:

• Label as security and @ mention @gitlab-com/gl-security/appsec
• The MR includes necessary changes to maintain consistency between UI, API, email, or other methods
• Security reports checked/validated by a reviewer from the AppSec team

Related to #288339 (closed)