Add first-class <shopify-account> support

Context

<shopify-account> is Shopify's Storefront Web Component for a customer-account avatar. When selected, it opens Shopify's account sheet with sign-in options or signed-in customer links. Shopify owns the interactive button, account sheet, authentication UI and client-side shadow DOM.

Hydrogen users currently need to load and integrate the component manually. This work adds first-class support with server-rendered signed-out content and stable layout before the custom element upgrades.

Scope

This parent issue tracks three independently reviewable deliverables:

1. Add opt-in account widget loading to ShopifyScripts.
2. Add a framework-neutral SSR-safe renderer and use it in the React Router template.
3. Add idiomatic React and Vue ShopifyAccountWidget bindings.

Agreed direction

• Name the ShopifyScripts opt-in accountWidget.
• Require a signed-out avatar so every integration has an SSR fallback and reserved layout space.
• Let the framework-neutral renderer accept required trusted avatar HTML. React accepts a required ReactElement; Vue exposes a required named slot.
• Hydrogen owns the slot="signed-out-avatar" wrapper so consumers cannot misconfigure Shopify's slot protocol.
• Emit a scoped nonce-bearing <style> that reserves the host and avatar dimensions with var(--shopify-account-avatar-size, 44px).
• Do not reproduce Shopify's private shadow DOM or use Declarative Shadow DOM.
• Listen directly on <shopify-account> for its non-bubbling open and close events.

Out of scope

• Customer Account OAuth, sessions or account pages.
• Reproducing or styling Shopify's internal account button or sheet.

References

• Hydrogen account component guide
• <shopify-account> API
• <shopify-store> API

Start by mapping the three deliverables named in the issue: accountWidget loading in ShopifyScripts, the framework-neutral SSR-safe renderer used by the React Router template, and the React and Vue bindings. Review the Shopify account and Shopify store API references first. Done means signed-out SSR content, reserved layout space, opt-in loading, and idiomatic bindings with the stated event behavior, without reproducing Shopify's private UI.