Build personal projects tab

What does this MR do and why?

Related to #378679 (closed)

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. This MR builds out some of the Personal projects section.

In future MRs we will:

1. Add MR count to each project
2. Add description to each project
3. Add topics to each project
4. Add pipeline status to each project
5. Add empty state

Some of these changes are waiting on API updates in !117079 (closed). But also I left them out to try and keep this MR as small as possible.

Screenshots or screen recordings

Loading state

Successfully loaded

Error state

How to set up and validate locally

1. Enable the profile_tabs_vue feature flag
   • bin/rails console
   • Feature.enable(:profile_tabs_vue)
2. Go to your profile

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.