feat(repo): Add Chrome Extension playground app [SDK-836]

[tmilewski]

Description

Adds a playground application for Chrome Extensions.

Checklist

• npm test runs as expected.
• npm run build runs as expected.
• (If applicable) JSDoc comments have been added or updated for any package exports
• (If applicable) Documentation has been updated

Type of change

• 🐛 Bug fix
• 🌟 New feature
• 🔨 Breaking change
• 📖 Refactoring / dependency upgrade / documentation
• other: Playground

Packages affected

• @clerk/backend
• @clerk/chrome-extension
• @clerk/clerk-js
• @clerk/clerk-expo
• @clerk/fastify
• gatsby-plugin-clerk
• @clerk/localizations
• @clerk/nextjs
• @clerk/clerk-react
• @clerk/remix
• @clerk/clerk-sdk-node
• @clerk/shared
• @clerk/themes
• @clerk/types
• build/tooling/chore

[changeset-bot]

⚠️ No Changeset found

Latest commit: 80ff394

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[dimkl]

Some time ago we were discussing dropping the playground directory. Since we haven't done it yet, let's proceed adding this playground.

[tmilewski]

@dimkl Agreed. I noticed that another was added somewhat recently. Considering that it's easy to move, I just kept it there for consistency.