feat(slice-1): Vite/React shell + /api proxy; scripts/check.sh now fully green

Single tsconfig (no project-references split — avoids composite/noEmit friction for
the minimal shell); tsc typechecks src, vite loads its config via esbuild.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

frontend/src/main.tsx

@@ -0,0 +1,9 @@
+import { StrictMode } from "react";
+import { createRoot } from "react-dom/client";
+import App from "./App";
+
+createRoot(document.getElementById("root")!).render(
+  <StrictMode>
+    <App />
+  </StrictMode>,
+);