feat(responses): implement full multi-turn support (#2295)

I think the implementation needs more simplification. Spent way too much
time trying to get the tests pass with models not co-operating :(
Finally had to switch claude-sonnet to get things to pass reliably.

### Test Plan

```
export TAVILY_SEARCH_API_KEY=...
export OPENAI_API_KEY=...

uv run pytest -p no:warnings \
   -s -v tests/verifications/openai_api/test_responses.py \
 --provider=stack:starter \
  --model openai/gpt-4o
```

docs/_static/llama-stack-spec.html

@@ -7283,6 +7283,9 @@
                         "items": {
                             "$ref": "#/components/schemas/OpenAIResponseInputTool"
                         }
+                    },
+                    "max_infer_iters": {
+                        "type": "integer"
                     }
                 },
                 "additionalProperties": false,

docs/_static/llama-stack-spec.yaml

@@ -5149,6 +5149,8 @@ components:
           type: array
           items:
             $ref: '#/components/schemas/OpenAIResponseInputTool'
+        max_infer_iters:
+          type: integer
       additionalProperties: false
       required:
         - input