feat(ai): Add $ai_framework property for framework integrations (#347)

* Add $ai_lib_metadata to AI integrations

Adds framework identification metadata to all AI events for easier filtering
and analytics. Each integration now includes a $ai_lib_metadata property with
schema version and framework name.

- LangChain: Hardcoded to "langchain"
- Native wrappers (Anthropic, OpenAI, Gemini): Uses provider name
- Ready for future frameworks (pydantic-ai, crewai, llamaindex)

This enables PostHog queries to easily distinguish between:
- Direct SDK wrapper usage
- Framework-mediated usage (LangChain, etc.)
- Different framework types

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

* Add \$ai_lib_metadata to sync/async paths and tests

- Added \$ai_lib_metadata to call_llm_and_track_usage (sync)
- Added \$ai_lib_metadata to call_llm_and_track_usage_async (async)
- Added test assertion in test_basic_completion
- Placed metadata at end of properties for consistency

All tests pass successfully.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

* Refactor: use unified utility function for $ai_lib_metadata

Creates a single `get_ai_lib_metadata(framework)` utility function to generate
the $ai_lib_metadata object, replacing inline implementations across the
codebase.

Changes:
- Add get_ai_lib_metadata() utility to utils.py
- Update LangChain callbacks to use utility function
- Update call_llm_and_track_usage() to use utility function
- Update call_llm_and_track_usage_async() to use utility function
- Update capture_streaming_event() to use utility function

Benefits:
- Consistency across all integrations
- Single source of truth for metadata structure
- Easier to extend with version detection later

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

* Add $ai_lib_metadata assertions to provider tests

Add missing $ai_lib_metadata assertions to Anthropic, Gemini, and LangChain tests to match the validation already present in OpenAI tests. Each test now verifies the metadata field contains the correct schema version and framework name.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

* Simplify to $ai_framework property, only for actual frameworks

Changes:
- Replace complex $ai_lib_metadata object with simple $ai_framework string
- Only include $ai_framework when using actual framework (LangChain)
- Remove $ai_framework from direct provider calls (OpenAI, Anthropic, Gemini)
- Update all tests to reflect new behavior

Before: {"schema": "v1", "frameworks": [{"name": "langchain"}]}
After: "langchain" (only when using LangChain framework)

This eliminates wasteful redundancy where framework=provider for direct calls.

---------

Co-authored-by: Claude <noreply@anthropic.com>

Author: andrewm4894

posthog/ai/langchain/callbacks.py

@@ -486,6 +486,7 @@ def _capture_trace_or_span(
             "$ai_latency": run.latency,
             "$ai_span_name": run.name,
             "$ai_span_id": run_id,
+            "$ai_framework": "langchain",
         }
         if parent_run_id is not None:
             event_properties["$ai_parent_id"] = parent_run_id
@@ -556,6 +557,7 @@ def _capture_generation(
             "$ai_http_status": 200,
             "$ai_latency": run.latency,
             "$ai_base_url": run.base_url,
+            "$ai_framework": "langchain",
         }
 
         if run.tools:

posthog/test/ai/langchain/test_callbacks.py

@@ -204,6 +204,7 @@ def test_basic_chat_chain(mock_client, stream):
     # Generation is second
     assert generation_args["event"] == "$ai_generation"
     assert "distinct_id" in generation_args
+    assert generation_props["$ai_framework"] == "langchain"
     assert "$ai_model" in generation_props
     assert "$ai_provider" in generation_props
     assert generation_props["$ai_input"] == [