Add example using autogen-core and FastAPI for handoff multi-agent design pattern with streaming and UI

[amith-ajith]

Why are these changes needed?

This PR adds an example which demonstrates how to build a streaming chat API with multi-turn conversation history and a simple web UI for handoff multi-agent design pattern.

Related issue number

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• [☑️ ] I've included any doc changes needed for https://microsoft.github.io/autogen/. See https://github.com/microsoft/autogen/blob/main/CONTRIBUTING.md to build and test documentation locally.
• [ ☑️] I've added tests (if relevant) corresponding to the changes introduced in this PR.
• [ ☑️] I've made sure all auto checks have passed.

[amith-ajith]

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 78.38%. Comparing base (d96aaeb) to head (d158436).
Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #6391   +/-   ##
=======================================
  Coverage   78.38%   78.38%           
=======================================
  Files         221      221           
  Lines       16024    16024           
=======================================
  Hits        12560    12560           
  Misses       3464     3464           

Flag	Coverage Δ
unittests	78.38% <ø> (ø)

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