lazy initialize the session upon stdio client initializes

[wzxxing]

Summary

Changes

Please provide a summary of what's being changed

There is new parameter auto_initialize added to the Client in fastmcp>=2.13.1 (https://github.com/jlowin/fastmcp/releases/tag/v2.13.1)

We need to use this parameter in the proxy because the proxy should accept initialize request from stdio, pass it to the fastmcp.Client so that the version and capabilities negotiated is what the actual client (such as kiro and kiro desktop) supports. Otherwise, the initialize will use the capability supported by fastmcp and it might mismatch with what the client uses.

User experience

Please share what the user experience looks like before and after this change

This is a fix for user experience. User should not experience hanging initialize request any more.

Checklist

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• I have reviewed the contributing guidelines
• I have performed a self-review of this change
• Changes have been tested
• Changes are documented

Is this a breaking change? (Y/N)

• Yes
• No

Please add details about how this change was tested.

• Did integration tests succeed?
• If the feature is a new use case, is it necessary to add a new integration test case?

Acknowledgment

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