docs: update GenAI structured output section to include JSON mode details (#32992)

Author: mdrxy

docs/docs/integrations/chat/google_generative_ai.ipynb

@@ -31,7 +31,7 @@
     "\n",
     "| [Tool calling](/docs/how_to/tool_calling) | [Structured output](/docs/how_to/structured_output/) | JSON mode | [Image input](/docs/how_to/multimodal_inputs/) | Audio input | Video input | [Token-level streaming](/docs/how_to/chat_streaming/) | Native async | [Token usage](/docs/how_to/chat_token_usage_tracking/) | [Logprobs](/docs/how_to/logprobs/) |\n",
     "| :---: | :---: | :---: | :---: |  :---: | :---: | :---: | :---: | :---: | :---: |\n",
-    "| ✅ | ✅ | ❌ | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ❌ |\n",
+    "| ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ❌ |\n",
     "\n",
     "### Setup\n",
     "\n",
@@ -653,15 +653,35 @@
     "\n",
     "# Initialize the model\n",
     "llm = ChatGoogleGenerativeAI(model=\"gemini-2.0-flash\", temperature=0)\n",
-    "structured_llm = llm.with_structured_output(Person)\n",
+    "\n",
+    "# Method 1: Default function calling approach\n",
+    "structured_llm_default = llm.with_structured_output(Person)\n",
+    "\n",
+    "# Method 2: Native JSON mode\n",
+    "structured_llm_json = llm.with_structured_output(Person, method=\"json_mode\")\n",
     "\n",
     "# Invoke the model with a query asking for structured information\n",
-    "result = structured_llm.invoke(\n",
+    "result = structured_llm_json.invoke(\n",
     "    \"Who was the 16th president of the USA, and how tall was he in meters?\"\n",
     ")\n",
     "print(result)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "g9w06ld1ggq",
+   "metadata": {},
+   "source": [
+    "### Structured Output Methods\n",
+    "\n",
+    "Two methods are supported for structured output:\n",
+    "\n",
+    "- **`method=\"function_calling\"` (default)**: Uses tool calling to extract structured data. Compatible with all Gemini models.\n",
+    "- **`method=\"json_mode\"`**: Uses Gemini's native structured output with `responseSchema`. More reliable but requires Gemini 1.5+ models.\n",
+    "\n",
+    "The `json_mode` method is **recommended for better reliability** as it constrains the model's generation process directly rather than relying on post-processing tool calls."
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "90d4725e",