fix: sanitize Claude auth subprocess environment

[vycdev2]

Summary

• sanitize the environment used by Claude authentication status and login subprocesses
• remove inherited CLAUDECODE markers case-insensitively so auth works when Claudify runs under Claude Code
• add regression coverage for both status and PTY-backed login paths

Verification

• npm run build — passed: TypeScript compilation completed
• npm test — passed: 110 tests
• git diff --check — passed

Risk

• Low: the change only copies the existing auth subprocess environment while omitting the nested-Claude marker, matching the response subprocess behavior.

This was generated by an AI agent (vycdev2). Please verify any changes before merging or applying.