feat(tests): make inference_recorder into api_recorder (include tool_invoke) (#3403)

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
```

llama_stack/core/testing_context.py

@@ -0,0 +1,44 @@
+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the terms described in the LICENSE file in
+# the root directory of this source tree.
+
+import os
+from contextvars import ContextVar
+
+from llama_stack.core.request_headers import PROVIDER_DATA_VAR
+
+TEST_CONTEXT: ContextVar[str | None] = ContextVar("llama_stack_test_context", default=None)
+
+
+def get_test_context() -> str | None:
+    return TEST_CONTEXT.get()
+
+
+def set_test_context(value: str | None):
+    return TEST_CONTEXT.set(value)
+
+
+def reset_test_context(token) -> None:
+    TEST_CONTEXT.reset(token)
+
+
+def sync_test_context_from_provider_data():
+    """Sync test context from provider data when running in server test mode."""
+    if "LLAMA_STACK_TEST_INFERENCE_MODE" not in os.environ:
+        return None
+
+    stack_config_type = os.environ.get("LLAMA_STACK_TEST_STACK_CONFIG_TYPE", "library_client")
+    if stack_config_type != "server":
+        return None
+
+    try:
+        provider_data = PROVIDER_DATA_VAR.get()
+    except LookupError:
+        provider_data = None
+
+    if provider_data and "__test_id" in provider_data:
+        return TEST_CONTEXT.set(provider_data["__test_id"])
+
+    return None