Add a TanStack Start Hydrogen storefront example

[liaoyio]

WHY are these changes introduced?

Hydrogen's preview repository validates its framework-agnostic commerce APIs through complete framework examples, but it does not yet include a TanStack Start integration. This example demonstrates TanStack Start's server functions, request lifecycle, router search state, and server/client boundaries against the same storefront behaviors as the existing examples.

WHAT is this pull request doing?

• Adds a TanStack Start storefront example organized consistently with the React Router example.
• Creates a request-scoped Hydrogen context for Storefront API, cart, customer account, analytics, and consent flows.
• Implements home, collections, collection filtering and sorting, product variants, search, cart, and customer account routes.
• Adds sitemap, robots, catch-all/404 handling, and personalized-response cache protections.
• Registers the example in repository documentation and the workspace lockfile.
• Excludes generated TanStack artifacts and the generated route tree from repository lint/format checks.
• Follows the existing framework-example convention without adding a package-local Vitest test suite.

HOW to test your changes?

From the repository root:

pnpm install --frozen-lockfile
pnpm run format:check
pnpm run lint:ci
pnpm run build
pnpm run typecheck
pnpm run test

For manual verification:

pnpm --filter @shopify/hydrogen-example-tanstack-start dev

Verify collection filter/sort and Back/Forward state, product variant selection, search, cart add/update/remove, customer account fallback, 404 handling, /robots.txt, and /sitemap.xml.

Checklist

• I've read the Contributing Guidelines
• I've considered possible cross-platform impacts (Mac, Linux, Windows)
• A changeset is not required because this private example package matches the configured @shopify/hydrogen-example-* ignore rule
• Testing is covered by the existing repository suite plus the example's typecheck and production build; framework examples do not carry package-local Vitest suites
• I've added or updated the documentation

[liaoyio]

I have signed the CLA!