🛠 Tooling: Modernize test suite

[JoshuaKGoldberg]

Tooling Report Checklist

• I have tried restarting my IDE and the issue persists.
• I have pulled the latest main branch of the repository.
• I have searched for related issues and found none that matched my issue.

Overview

Right now, tests are a cobbled-together conglomeration of Mocha, Chai, Sinon, and a wrapper or two to get them running in the browser. I'd like to get something more modern & standard. Maybe, Vitest browser mode?

Needs investigation.

Additional Info

No response