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/vite.config.ts

@@ -0,0 +1,18 @@
+import { defineConfig } from "vite";
+import react from "@vitejs/plugin-react";
+
+// The SPA talks to the FastAPI backend on :8000 via a same-origin proxy, so the
+// browser makes no cross-origin calls in dev. Override the target with
+// VITE_API_TARGET when :8000 is occupied. Screen-shaped /api/* endpoints arrive in
+// SLICE-2/3 (SD-0001 §6.4).
+const apiTarget = process.env.VITE_API_TARGET || "http://localhost:8000";
+
+export default defineConfig({
+  plugins: [react()],
+  server: {
+    port: 5173,
+    proxy: {
+      "/api": apiTarget,
+    },
+  },
+});