Add client info to instrumentation callback

[duboff]

Motivation and Context

Adding client information to the instrumentation callback. A follow-up to #218 of sorts. Client info is very helpful for analytics and debugging purposes.

How Has This Been Tested?

Yes, tested with the Chattermill MCP (proprietary).

Breaking Changes

No breaking changes

Types of changes

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

Checklist

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

Additional context