[MVC] Context switcher opportunities for improvement

Problem to solve

During the GitLab Team Member dogfooding, we got some feedback about the context switcher being somewhat confusing in some situations.

Two things stood out –

• It's not clear what the context switcher actually does: !113256 (comment 1305976982).
• Some labels within the context switcher are confusing: #405033 (closed)

Proposal

Move the context switcher body into a dropdown and clean up the styles.

Next steps

Add context switcher items to global search mod... (#409522 - closed) • Mark Florian • 16.3