feat: add SPA, serve at /app/, update Dockerfile and README

- React + TanStack Router + shadcn/ui SPA under spa/
- serve spa/dist at /app/ with index.html fallback for client routing
- Dockerfile: node build stage for SPA, copy dist into runtime image
- README: document SPA, CORS_ORIGINS env var, architecture entry
- vite base set to /app/, manifest.json paths fixed

spa/src/routes/__root.tsx

@@ -0,0 +1,14 @@
+import { createRootRoute, Outlet } from "@tanstack/react-router"
+import { ThemeProvider } from "@/components/theme-provider"
+
+export const Route = createRootRoute({
+  component: RootLayout,
+})
+
+function RootLayout() {
+  return (
+    <ThemeProvider>
+      <Outlet />
+    </ThemeProvider>
+  )
+}