Move Vue user profile from tabs to Vue router

What does this MR do and why?

In &9056 we are migrating the user profile from HAML/jQuery to Vue. This is a large migration so we are splitting it up into many sections. We started this migration with tabs because, at the time, that is what the existing page used. But after starting the migration we learned that we were planning on moving away from tabs and having the navigation in the sidebar. This MR builds on top of !119838 (merged) and migrates from tabs to Vue router.

Screenshots or screen recordings

Screen_Recording_2023-05-12_at_7.06.40_AM

How to set up and validate locally

Numbered steps to set up and validate the change are strongly suggested.

MR acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• I have evaluated the MR acceptance checklist for this MR.

Related to #389842