feat(website): migrate website to TanStack Start

[nedanwr]

Summary

Migrates the website app from Next.js to TanStack Start/Vite for the 0.5.x release line.

Changes

• Replaced Next.js build/runtime tooling with TanStack Start, TanStack Router, and Vite
• Migrated home, docs, playground, search API, LLM text, and OG image routes into TanStack file routes
• Updated Fumadocs MDX/source wiring for TanStack Start server/client loading
• Added generated TanStack route tree and router setup
• Updated website package version to 0.5.0
• Switched Fumadocs styling to compiled fumadocs-ui/style.css to avoid dev-only Tailwind @apply failures
• Hardened checkout credentials in .github/workflows/test.yml

Testing

• All existing tests pass
• New tests added (if applicable)
• Examples updated (if applicable)
• Memory leak checks pass (if applicable)

Verified manually:

• pnpm build
• pnpm types:check
• pnpm lint
• Dev smoke checks for /, /docs, /docs/getting-started, /playground
• Endpoint checks for /api/search?query=variable, /llms-full.txt, /og/docs/getting-started/image.png
• Verified missing docs route returns 404

Documentation

• Examples updated (if applicable)
• README/docs updated (if applicable)

No documentation changes in this PR.

Breaking Changes

Website runtime/build tooling changes from Next.js to TanStack Start/Vite.

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Project	Deployment	Actions	Updated (UTC)
kronos	Error		Jul 10, 2026 5:45am

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✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Commit unit tests in branch feat/website-tanstack-start

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