## Why
`connector_auth_failure_from_tool_result` requires an install URL to return an auth failure, even when the tool result contains valid auth failure metadata.
## What changed
Export `is_connector_auth_failure_from_tool_result` from `codex-mcp` to detect auth failures independently of an install URL. Share metadata validation with the existing parser, requiring an error result, an explicit auth failure flag, and a nonempty connector ID that does not conflict with the metadata.
## Testing
Add unit tests for detection without an install URL, rejection of missing or mismatched connector identities and non-auth errors or successful results, and detection for all three supported auth reasons.
GitOrigin-RevId: 6e4e177f26d9a34c56874b0360bae63f6c89107e