docs: describe stderr as the general logging channel for stdio servers #3037

Where was this agreed?

Requested by maintainer David Soria Parra as part of preparing the modelcontextprotocol.io documentation for the 2026-07-28 specification release.

Description

As of the 2026-07-28 spec release, stdio servers may use stderr for all logging, not just errors. Two develop guides still describe stderr output as error-only.

Files to update:

• docs/docs/develop/connect-local-servers.mdx — reword "error (stderr) logging" (line 234) to describe all stderr output
• docs/docs/develop/build-server.mdx — same rewording in the desktop-app troubleshooting accordion (~line 3022)

Part of the 2026-07-28 release documentation tracking (milestone: 2026-07-28 Specification Release).