Fix Cycle Analytics landing widget state and improve state management in Vue.

What does this MR do?

• Fixes Cycle Analytics help widget show/hide issue
• Addresses initial MR feedback with improving Vue state management logic
• Fixes cookie path of the help widget so when you close a help widget in a repo it won't be visible for other repos.

Are there points in the code the reviewer needs to double check?

• Should we move gl.cycleAnalyticsModel to a new file.

Why was this MR needed?

• Addresses feedbacks of initial MR and fixes #22483 (closed)

Screenshots (if relevant)

Does this MR meet the acceptance criteria?

• CHANGELOG entry added
• Documentation created/updated
• API support added
• Tests
  • Added for this feature/bug
  • All builds are passing
• Conform by the merge request performance guides
• Conform by the style guides
• Branch has no merge conflicts with master (if you do - rebase it please)
• Squashed related commits together

What are the relevant issue numbers?

Fixes #22483 (closed)