Add interactive patient web app

[agr-333]

Summary

• add a FastAPI-powered web API with endpoints for starting sessions, sending doctor messages, and revealing diagnoses
• implement a lightweight dataset-driven patient conversation session manager
• provide a single-page interface with styling, client logic, and documentation updates for running the demo

Testing

• python -m compileall medsim/webapp
• python - <<'PY'
  from medsim.webapp.session import SessionManager
  manager = SessionManager()
  session = manager.create_session()
  print('Session ID:', session.session_id)
  print('Initial message:', session.history[-1]['content'][:120])
  reply, state = manager.handle_message(session.session_id, 'Can you tell me about the physical exam?')
  print('Reply snippet:', reply[:120])
  print('Shared exam:', state['metadata']['progress']['shared_exam'])
  print('Diagnosis:', manager.reveal(session.session_id))
  PY

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https://chatgpt.com/codex/tasks/task_e_68f8d94792e4832d908d4effd63a7f86