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

[perk11]

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

[perk11]

Additionally, it would be great if it would fail right after the process exits and wouldn't wait for the timeout.