fix(chat): use native async LLM call to prevent session reset on message submit

The previous implementation used asyncio.to_thread(llm.complete) to avoid
blocking the event loop, but Chainlit's contextvars context is not reliably
propagated across thread boundaries, causing the session to reset and clear
the message history on each user submission.

Changes:
- Add llm.acomplete() using litellm.acompletion() (native coroutine)
- Replace asyncio.to_thread() in on_message with await llm.acomplete()
- Store the welcome message in state.messages so it is replayed on reconnect
- Persist state to cl.user_session immediately after appending the user's
  message (before the LLM call) so reconnect detection has the latest history
- Add pytest-asyncio dev dependency and asyncio_mode = "auto" config
- Add 6 async tests for acomplete() in tests/test_llm.py

https://claude.ai/code/session_01SUWzMzFvSfWiHXA2p6rPg9

pyproject.toml

@@ -26,5 +26,9 @@ packages = ["src"]
 [tool.uv]
 dev-dependencies = [
     "pytest>=8.0.0",
+    "pytest-asyncio>=1.3.0",
     "pytest-mock>=3.14.0",
 ]
+
+[tool.pytest.ini_options]
+asyncio_mode = "auto"