Switch chatbot to use the langgraph Functional API

[JoshuaC215]

Roughly following the example in https://langchain-ai.github.io/langgraph/how-tos/persistence-functional/

But sticking with the "messages" key to maintain API compatibility with the other agents.

[codecov]

Codecov Report

Attention: Patch coverage is 50.00000% with 6 lines in your changes missing coverage. Please review.

Project coverage is 68.08%. Comparing base (00e69b3) to head (ea319b6).
Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/agents/chatbot.py	50.00%	6 Missing ⚠️

Files with missing lines	Coverage Δ
src/agents/chatbot.py	57.14% <50.00%> (-12.86%)	⬇️

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