examples/nextjs: server components + Suspense streaming for home & header

[malewis5]

Stacked on #3811 — this PR is based on the `lib/`+`components/` hoist in #3811. GitHub shows a cumulative diff until #3811 merges; review the home/header commits only, and merge #3811 first.

WHY are these changes introduced?

The Next.js example used patterns that block streaming and aren't idiomatic App Router: a "use client" header with prop-drilled data, a force-dynamic layout that blocks on cart + collections before anything paints, and a home page that awaits all products before rendering the hero.

This restructures the example toward idiomatic App Router data-fetching and streaming — and toward cacheComponents — without touching the @shopify/hydrogen core.

WHAT is this pull request doing?

• Client islands: extract CartButton so Header is a server component that fetches its own collections — no "use client" on the header, no prop-drilling from the layout.
• Streaming: split the home grid into a static ProductListShell + a <Suspense>-streamed ProductList with a skeleton fallback, so the hero paints before products resolve.
• Non-blocking layout: drop force-dynamic and the blocking cart/collections fetch from the root layout. Data is colocated in the components that need it; getStorefrontClient stays React.cache()-memoized so shared calls dedupe within a request.
• Cart: CartProvider seeds client-side via its built-in fetch instead of a blocking server seed, keeping the layout streamable. A Providers TODO documents the promise + React.use() path that would restore an SSR'd cart count (needs a core change, deferred).

HOW to test your changes?

1. pnpm run dev:next
2. Home, collections, and product pages render; the hero paints immediately while the product grid streams in behind its skeleton.
3. Cart count hydrates client-side; add/update via the cart drawer works.

pnpm run check (format, lint, typecheck, test) passes.

Follow-ups (toward Cache Components)

• Wrap Header's collections in <Suspense> so the nav shell doesn't block the layout (and won't taint the route under cacheComponents).
• Enable cacheComponents + use cache on catalog fetches — requires splitting headers() out of getStorefrontClient so catalog queries (no per-request input) become cacheable, separate from cart / buyer-IP (dynamic).

Checklist

• I've read the Contributing Guidelines
• I've considered possible cross-platform impacts (Mac, Linux, Windows)
• I've added a changeset — N/A, example-only change to a private package
• I've added tests — N/A, example app
• I've added or updated the documentation

[malewis5]

I have signed the CLA!

[benjaminsehl]

Thanks, Matt!

[fredericoo]

thank you for the contribution! it all works as expected. looks like our generated code was misusing next a little bit

[fredericoo]

lol i read it backwards, thought it was to merge this one first. will fix it on my end!