[Client] Print contents of stderr when command in StdioTransport fails to start

Is your feature request related to a problem? Please describe.
Currently when command fails to start all I get is "Error Initialization failed: Request timed out", which is hard to debug.

Describe the solution you'd like
Print a more specific error message and the contents of stderr that was outputted when starting the MCP server

Describe alternatives you've considered
Add debugging code to library source or use xdebug

まず、Client StdioTransport の起動パスと、コマンドの失敗がどのように "Request timed out" エラーになるかを特定します。コマンドの起動中に stderr がどのように取得されるかを追跡し、次に、MCP サーバーの起動に失敗した場合に stderr の内容を含む具体的なエラーが報告されることを確認します。