docs(genai): enhance structured output methods docstring (#1186)

Author: mdrxy

libs/genai/langchain_google_genai/chat_models.py

@@ -1216,8 +1216,12 @@ class Joke(BaseModel):
                 )
 
 
+            # Default method uses function calling
             structured_llm = llm.with_structured_output(Joke)
-            structured_llm.invoke("Tell me a joke about cats")
+
+            # For more reliable output, use json_mode with native responseSchema
+            structured_llm_json = llm.with_structured_output(Joke, method="json_mode")
+            structured_llm_json.invoke("Tell me a joke about cats")
 
         .. code-block:: python
 
@@ -1227,6 +1231,17 @@ class Joke(BaseModel):
                 rating=None,
             )
 
+        Two methods are supported for structured output:
+
+        * ``method="function_calling"`` (default): Uses tool calling to extract
+        structured data. Compatible with all models.
+        * ``method="json_mode"``: Uses Gemini's native structured output with
+        responseSchema. More reliable but requires Gemini 1.5+ models.
+
+        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.
+
     Image input:
         .. code-block:: python