Move state from root instance to Vuex

What does this MR do?

• Follow-up to !40548 (merged)
• Part of &4233 (closed)

Originally I setup this app to store the state in the root instance. After some more development (not merged yet), I have realized that it is going to be easier to manage state in a Vuex store.

More specifically, later in development, the expiration date and user role will need to be updated after making an API call. This will be much easier if we can dispatch an action that makes the API call and then commits a mutation that updates the member.

Screenshots

No visual changes

Does this MR meet the acceptance criteria?

Conformity

• Changelog entry
  • Not needed, backstage change and behind a feature flag
• [-] 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