feat: enable MCP execution in Responses impl (#2240)

## Test Plan

```
pytest -s -v 'tests/verifications/openai_api/test_responses.py' \
  --provider=stack:together --model meta-llama/Llama-4-Scout-17B-16E-Instruct
```

.github/workflows/integration-tests.yml

@@ -24,7 +24,7 @@ jobs:
       matrix:
         # Listing tests manually since some of them currently fail
         # TODO: generate matrix list from tests/integration when fixed
-        test-type: [agents, inference, datasets, inspect, scoring, post_training, providers]
+        test-type: [agents, inference, datasets, inspect, scoring, post_training, providers, tool_runtime]
         client-type: [library, http]
       fail-fast: false # we want to run all tests regardless of failure
 
@@ -90,7 +90,7 @@ jobs:
           else
             stack_config="http://localhost:8321"
           fi
-          uv run pytest -v tests/integration/${{ matrix.test-type }} --stack-config=${stack_config} \
+          uv run pytest -s -v tests/integration/${{ matrix.test-type }} --stack-config=${stack_config} \
             -k "not(builtin_tool or safety_with_image or code_interpreter or test_rag)" \
             --text-model="meta-llama/Llama-3.2-3B-Instruct" \
             --embedding-model=all-MiniLM-L6-v2