fix: use the json rpc error from the initialize response and bubble up to the client

[tonyxwz]

Motivation and Context

Returns the error when initialization response is a json rpc error. Otherwise the client would be waiting in the loop and hangs until timeout.

fixes: #563

Before the change:

• If the server sent a JSON-RPC error during initialization, it fell through to the catch-all _ pattern
• The error was only logged with tracing::warn! and ignored
• The client would hang waiting for a valid response that never comes
• User gets a timeout or connection closed error instead of the actual error

After the change:

• JSON-RPC error is caught and converted to ClientInitializeError::JsonRpcError
• The error propagates up through the ? operator at line 241: .await?
• Returns immediately from serve_client_with_ct_inner with the error
• User receives Err(ClientInitializeError::JsonRpcError(error_data)) from .serve()
• User can see the actual error code and message from the server

How Has This Been Tested?

Breaking Changes

This is not a breaking change. But it should fix the issues where the client response with a default error message when the session connection failed.

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