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/tsconfig.json

@@ -0,0 +1,12 @@
+{
+  "files": [],
+  "references": [
+    { "path": "./tsconfig.app.json" },
+    { "path": "./tsconfig.node.json" }
+  ],
+  "compilerOptions": {
+    "paths": {
+      "@/*": ["./src/*"]
+    }
+  }
+}