Enhancement: make stderr of server subprocess configurable (#191)

* make stderr of server subprocess configurable

* Update stdio.py

---------

Co-authored-by: David Soria Parra <167242713+dsp-ant@users.noreply.github.com>

src/mcp/client/stdio.py

@@ -2,7 +2,7 @@ import os
 import sys
 from contextlib import asynccontextmanager
 from pathlib import Path
-from typing import Literal
+from typing import Literal, TextIO
 
 import anyio
 import anyio.lowlevel
@@ -87,7 +87,7 @@ class StdioServerParameters(BaseModel):
 
 
 @asynccontextmanager
-async def stdio_client(server: StdioServerParameters):
+async def stdio_client(server: StdioServerParameters, errlog: TextIO = sys.stderr):
     """
     Client transport for stdio: this will connect to a server by spawning a
     process and communicating with it over stdin/stdout.
@@ -104,7 +104,7 @@ async def stdio_client(server: StdioServerParameters):
     process = await anyio.open_process(
         [server.command, *server.args],
         env=server.env if server.env is not None else get_default_environment(),
-        stderr=sys.stderr,
+        stderr=errlog,
         cwd=server.cwd,
     )