🛠 Tooling: Create a more formal design system infrastructure

[JoshuaKGoldberg]

Tooling Report Checklist

• [X] I have pulled the latest main branch of the repository.
• [X] I have searched for related issues and found none that matched my request.
• [X] This is the appropriate issue form for the tooling issue I would like to report.

Expected

Right now this site uses the built-in CSS modules setup from Docusaurus. It gets the job done.

Actual

I'd like to do a deep dive on available design system builders (Chakra UI, styled-system, etc.) and use one for this site.

Additional Info

Blocked on the same factors as #15. I'm thinking I'll probably tackle this one after #15 is done.