feat(playground): deploy playground to GitHub Pages with extension detection

[naji247]

Summary

This PR makes the playground publicly accessible and adds Chrome extension awareness to improve the onboarding experience.

GitHub Pages deployment

• New deploy-playground.yml workflow builds the playground and deploys it to GitHub Pages on every push to main
• The playground is served at https://mcpcat.github.io/webmcp-react/playground/ — Vite's base is conditionally set via a GITHUB_PAGES env var so local dev remains unaffected
• The workflow uses actions/upload-pages-artifact and actions/deploy-pages with proper permissions and concurrency settings

Chrome extension detection

• New ExtensionBanner component that probes for the WebMCP Bridge extension using the existing window.postMessage protocol (WEBMCP_REQUEST_TOOLS → WEBMCP_TOOLS_UPDATED)
• Three states: checking (hidden, during the 2s detection window), connected (green banner), and not detected (amber banner with a Chrome Web Store install link)
• The amber banner is dismissible; the green banner is always visible when connected
• The Chrome Web Store URL is a placeholder (TODO comment) until the extension is published

Housekeeping

• Added noEmit: true to the playground's tsconfig.json so tsc -b only type-checks without emitting .js artifacts alongside source
• Added .gitignore patterns for src/**/*.js and examples/*/src/**/*.js to catch any stray tsc output
• Added a Playground section to the README with a link to the live demo

Test plan

• Run pnpm dev:playground and verify the playground loads at http://localhost:5173/
• Without the Chrome extension installed: after ~2s, an amber banner appears with a link to install the extension
• With the Chrome extension loaded and active on the tab: a green "WebMCP Bridge extension connected" banner appears
• Click the dismiss button (×) on the amber banner and confirm it disappears
• Run GITHUB_PAGES=true pnpm --filter webmcp-react-playground build and inspect dist/index.html to confirm asset paths reference /webmcp-react/playground/
• Verify CI passes on the PR
• After merge, confirm the playground is live at https://mcpcat.github.io/webmcp-react/playground/