fix(node-player): proxy /api through vite dev server for same-origin SW

Service Worker only intercepts same-origin requests. In dev mode, API
calls went directly to localhost:8085 (cross-origin), bypassing the SW.
Now vite proxies /api to Rust API, keeping everything same-origin so
the SW can inject Bearer tokens for audio/image requests.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

furumi-node-player/client/.env.example

@@ -1 +1,2 @@
-VITE_FURUMI_API_URL=http://localhost:8085
+# Leave empty — vite proxy handles /api in dev, same-origin in production
+VITE_FURUMI_API_URL=

furumi-node-player/client/vite.config.ts

@@ -14,6 +14,10 @@ export default defineConfig({
         target: 'http://localhost:3001',
         changeOrigin: true,
       },
+      '/api': {
+        target: 'http://localhost:8085',
+        changeOrigin: true,
+      },
     },
   },
 })