feat: wire workspace CRUD UI to backend

Co-Authored-By: Claude <noreply@anthropic.com>

web/vite.config.ts

@@ -3,6 +3,12 @@ import react from "@vitejs/plugin-react";
 import tailwindcss from "@tailwindcss/vite";
 import { defineConfig } from "vite";
 
+// In dev the frontend runs on its own port; proxy API calls to the Go backend
+// so the browser sees same-origin requests. In production the Go binary serves
+// the built assets directly and no proxy is involved.
+const backendTarget =
+  process.env.VITE_BACKEND_URL ?? "http://localhost:8080";
+
 export default defineConfig({
   plugins: [react(), tailwindcss()],
   resolve: {
@@ -10,4 +16,10 @@ export default defineConfig({
       "@": path.resolve(__dirname, "./src"),
     },
   },
+  server: {
+    proxy: {
+      "/api": { target: backendTarget, changeOrigin: true },
+      "/healthz": { target: backendTarget, changeOrigin: true },
+    },
+  },
 });