[FEATURE] Add per-MCP-server log files

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

I'm trying to write a stdin mcp server and finding the complete lack of errors or warnings from Claude Code a hindrance. I wish I had per-server logs of the interactions so I could better debug my server.

Proposed Solution

I'd like an --mcp-debug flag or something similar to log interactions, warnings, and errors, ideally saved somewhere convenient with per-server files.

Alternative Solutions

_No response_

Priority

Critical - Blocking my work

Feature Category

CLI commands and flags

Use Case Example

_No response_

Additional Context

Duplicate of auto-closed and auto-locked https://github.com/anthropics/claude-code/issues/29035