docs: stdio transport - explicit use of stderr for logging (modelcontextprotocol#670)

* docs: stdio transport - explicit use of stderr for logging

* docs: clearer instructions for how clients handle stderr

---------

Co-authored-by: Felix Weinberger <[email protected]>

Author: dwmkerr

docs/specification/draft/basic/transports.mdx

@@ -28,8 +28,10 @@ In the **stdio** transport:
   to its standard output (`stdout`).
 - Messages are individual JSON-RPC requests, notifications, or responses.
 - Messages are delimited by newlines, and **MUST NOT** contain embedded newlines.
-- The server **MAY** write UTF-8 strings to its standard error (`stderr`) for logging
-  purposes. Clients **MAY** capture, forward, or ignore this logging.
+- The server **MAY** write UTF-8 strings to its standard error (`stderr`) for any
+  logging purposes including informational, debug, and error messages.
+- The client **MAY** capture, forward, or ignore the server's `stderr` output
+  and **SHOULD NOT** assume `stderr` output indicates error conditions.
 - The server **MUST NOT** write anything to its `stdout` that is not a valid MCP message.
 - The client **MUST NOT** write anything to the server's `stdin` that is not a valid MCP
   message.