Chatbot example: clean up servers in correct order

[clareliguori]

The servers's async context must be exited in the reverse order it was entered, unrolling the context stack.

Motivation and Context

Fixes #252

How Has This Been Tested?

$ python main.py 
You: quit
2025-03-23 08:46:26,961 - INFO - 
Exiting...
$ echo $?
0

Breaking Changes

No

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation update

Checklist

• I have read the MCP Documentation
• My code follows the repository's style guidelines
• New and existing tests pass locally
• I have added appropriate error handling
• I have added or updated documentation as needed

Additional context

[pagoenka]

Can confirm that this fixes the issues like - #252, but this will cleanup the servers sequentially