Swap custom store for vuex implementation in merge_conflicts

What does this MR do?

This MR swaps the custom store with the new vuex implementation and remove the old and unused store and service.

Plan

Description	MR
Add new store	!55524 (merged)
Add basic tests for Utility, getters and mutation	!56494 (merged)
Wire the new store in the components and remove old one	👈 you are here

Screenshots (strongly suggested)

No visual changes but here is a video (my GDK was a bit slow in the end):

MergeConflicts

Does this MR meet the acceptance criteria?

Conformity

• 📋 Does this MR need a changelog?
  • I have included a changelog entry.
  • I have not included a changelog entry because this is a refactor.
• [-] 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