Python: Added thread to AgentRunContext (#1732)

* Added thread to agent run context

* Added sample

* Update python/samples/getting_started/middleware/thread_behavior_middleware.py

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

* Small fix

---------

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

python/samples/getting_started/middleware/README.md

@@ -13,6 +13,7 @@ This folder contains examples demonstrating various middleware patterns with the
 | [`exception_handling_with_middleware.py`](exception_handling_with_middleware.py) | Demonstrates how to use middleware for centralized exception handling in function calls. Shows how to catch exceptions from functions, provide graceful error responses, and override function results when errors occur to provide user-friendly messages. |
 | [`override_result_with_middleware.py`](override_result_with_middleware.py) | Shows how to use middleware to intercept and modify function results after execution, supporting both regular and streaming agent responses. Demonstrates result filtering, formatting, enhancement, and custom streaming response generation. |
 | [`shared_state_middleware.py`](shared_state_middleware.py) | Demonstrates how to implement function-based middleware within a class to share state between multiple middleware functions. Shows how middleware can work together by sharing state, including call counting and result enhancement. |
+| [`thread_behavior_middleware.py`](thread_behavior_middleware.py) | Demonstrates how middleware can access and track thread state across multiple agent runs. Shows how `AgentRunContext.thread` behaves differently before and after the `next()` call, how conversation history accumulates in threads, and timing of thread message updates. Essential for understanding conversation flow in middleware. |
 | [`agent_and_run_level_middleware.py`](agent_and_run_level_middleware.py) | Explains the difference between agent-level middleware (applied to ALL runs of the agent) and run-level middleware (applied to specific runs only). Shows security validation, performance monitoring, and context-specific middleware patterns. |
 | [`chat_middleware.py`](chat_middleware.py) | Demonstrates how to use chat middleware to observe and override inputs sent to AI models. Shows how to intercept chat requests, log and modify input messages, and override entire responses before they reach the underlying AI service. |
 
@@ -42,4 +43,4 @@ This folder contains examples demonstrating various middleware patterns with the
 
 - **Termination**: Use `context.terminate` to stop execution early
 - **Result Override**: Modify or replace function/agent results
-- **Streaming Support**: Handle both regular and streaming responses
+- **Streaming Support**: Handle both regular and streaming responses