fix: Structured outputs for recursive models (#1311)

Handle recursive nature in the structured response_formats. 

Update test to include 1 nested model.

```
 LLAMA_STACK_CONFIG=dev pytest -s -v tests/client-sdk/inference/test_text_inference.py --inference-model "openai/gpt-4o-mini" -k test_text_chat_completion_structured_output
```

---------

Co-authored-by: Ashwin Bharambe <ashwin.bharambe@gmail.com>

llama_stack/providers/tests/test_cases/inference/chat_completion.json

@@ -111,7 +111,8 @@
         "first_name": "Michael",
         "last_name": "Jordan",
         "year_of_birth": 1963,
-        "num_seasons_in_nba": 15
+        "num_seasons_in_nba": 15,
+        "year_for_draft": 1984
       }
     }
   },

llama_stack/providers/utils/inference/litellm_openai_mixin.py

@@ -126,6 +126,37 @@ class LiteLLMOpenAIMixin(
         ):
             yield chunk
 
+    def _add_additional_properties_recursive(self, schema):
+        """
+        Recursively add additionalProperties: False to all object schemas
+        """
+        if isinstance(schema, dict):
+            if schema.get("type") == "object":
+                schema["additionalProperties"] = False
+
+                # Add required field with all property keys if properties exist
+                if "properties" in schema and schema["properties"]:
+                    schema["required"] = list(schema["properties"].keys())
+
+            if "properties" in schema:
+                for prop_schema in schema["properties"].values():
+                    self._add_additional_properties_recursive(prop_schema)
+
+            for key in ["anyOf", "allOf", "oneOf"]:
+                if key in schema:
+                    for sub_schema in schema[key]:
+                        self._add_additional_properties_recursive(sub_schema)
+
+            if "not" in schema:
+                self._add_additional_properties_recursive(schema["not"])
+
+            # Handle $defs/$ref
+            if "$defs" in schema:
+                for def_schema in schema["$defs"].values():
+                    self._add_additional_properties_recursive(def_schema)
+
+        return schema
+
     async def _get_params(self, request: ChatCompletionRequest) -> dict:
         input_dict = {}
 
@@ -140,6 +171,10 @@ class LiteLLMOpenAIMixin(
             name = fmt["title"]
             del fmt["title"]
             fmt["additionalProperties"] = False
+
+            # Apply additionalProperties: False recursively to all objects
+            fmt = self._add_additional_properties_recursive(fmt)
+
             input_dict["response_format"] = {
                 "type": "json_schema",
                 "json_schema": {

tests/client-sdk/inference/test_text_inference.py

@@ -4,6 +4,7 @@
 # This source code is licensed under the terms described in the LICENSE file in
 # the root directory of this source tree.
 
+
 import pytest
 from pydantic import BaseModel
 
@@ -342,11 +343,15 @@ def test_text_chat_completion_with_tool_choice_none(client_with_models, text_mod
     ],
 )
 def test_text_chat_completion_structured_output(client_with_models, text_model_id, test_case):
+    class NBAStats(BaseModel):
+        year_for_draft: int
+        num_seasons_in_nba: int
+
     class AnswerFormat(BaseModel):
         first_name: str
         last_name: str
         year_of_birth: int
-        num_seasons_in_nba: int
+        nba_stats: NBAStats
 
     tc = TestCase(test_case)
 
@@ -364,7 +369,8 @@ def test_text_chat_completion_structured_output(client_with_models, text_model_i
     assert answer.first_name == expected["first_name"]
     assert answer.last_name == expected["last_name"]
     assert answer.year_of_birth == expected["year_of_birth"]
-    assert answer.num_seasons_in_nba == expected["num_seasons_in_nba"]
+    assert answer.nba_stats.num_seasons_in_nba == expected["num_seasons_in_nba"]
+    assert answer.nba_stats.year_for_draft == expected["year_for_draft"]
 
 
 @pytest.mark.parametrize("streaming", [True, False])