Use badge component for "busy" status

What does this MR do and why?

• Use badge component for busy status
• Why? It looks cleaner and draws attention to the status

What does this MR not do?

• Update when/where the busy status shows up (for example, it doesn't show up on the Reviewers section in MR sidebar)
• Update the width of the user dropdown. If the username is on the longer side, you may not see the Busy badge at all (existing functionality)
• Change tooltips- they'll still say Username (Busy)

TODO:

• MR/issue dropdown
• Issue board dropdown
• User popover
• Review areas where the badge doesn't show up (for example, why Assignee and notReviewers in MRs? Why does it not show up in the Issue sidebar at all? Separate issue
• Is warning the correct variant?

Screenshots or screen recordings

Before	After

How to set up and validate locally

#394879 (closed)

#321466 (closed)