Add the first-party icon catalog to the Playground and Docs

[konojunya]

Summary

• update the Playground to the public @stack-sh/engine@0.3.0 package and use the web explicit icon in the initial source
• document all 12 provider-neutral icon IDs, stable subjects, fallback behavior, and the vendor-icon boundary in English, Japanese, Simplified Chinese, and Korean
• add a searchable VitePress gallery that renders every icon locally with the published Engine, supports light/dark previews, and copies the exact Stack syntax
• validate the exact Engine pin, localized catalog coverage, SSR card output, and bundled Documentation WebAssembly

Verification

• npm run format:check
• npm run lint
• npm test (11 tests)
• npm run build (44 documentation pages)
• npm run cloudflare:check
• isolated Chrome QA at 1440px, 1024px, and 320px: 12 rendered cards in all four locales, light/dark toggle, copy action, local search, accessibility tree, Engine 0.3.0 / Theme Catalog 0.2.0 metadata, WebAssembly 200, no horizontal overflow, and no console or network errors
• Playground Chrome QA at 1440px and 320px: explicit web icon source, successful render, no diagnostics, Engine 0.3.0, WebAssembly 200, no horizontal overflow, and no console or network errors