Renames `inference_recorder.py` to `api_recorder.py` and extends it to
support recording/replaying tool invocations in addition to inference
calls.
This allows us to record web-search, etc. tool calls and thereafter
apply recordings for `tests/integration/responses`
## Test Plan
```
export OPENAI_API_KEY=...
export TAVILY_SEARCH_API_KEY=...
./scripts/integration-tests.sh --stack-config ci-tests \
--suite responses --inference-mode record-if-missing
```
