fix: inject part into extension when handing init req

[4t145]

Motivation and Context

fix #274

How Has This Been Tested?

Breaking Changes

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

[Copilot]

Pull Request Overview

Fixes the missing injection of part into the request extensions when handling initialization requests, addressing issue #274.

• Inject part into InitializeRequest extensions in two server paths.
• Introduce unexpected_message_response to handle non-initialization messages.
• Update imports to include ClientRequest.

Reviewed Changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 2 comments.

File	Description
crates/rmcp/src/transport/streamable_http_server/tower.rs	Added extension injection and unexpected-message checks
crates/rmcp/src/transport/common/server_side_http.rs	Added unexpected_message_response helper for 422 errors

Comments suppressed due to low confidence (2)

crates/rmcp/src/transport/common/server_side_http.rs:111

• [nitpick] Consider updating the error message to use 'expected' instead of 'expect' for grammatical clarity, e.g., 'Unexpected message, expected {expect}'.

        .body(Full::new(Bytes::from(format!("Unexpected message, expect {expect}"))).boxed_unsync())

crates/rmcp/src/transport/common/server_side_http.rs:106

• No tests cover the new unexpected_message_response path; consider adding unit tests to validate its status code and message content.

pub(crate) fn unexpected_message_response(