[deep-report] Fix GitHub Remote MCP auth test returning empty gh api output

[github-actions]

Description: The GitHub Remote MCP Authentication Test failed with gh api returning empty output despite exit code 0. Review the workflow token permissions and MCP server availability, and add explicit auth validation or a local-mode fallback to avoid silent failures.

Expected Impact: Restores daily MCP auth coverage and prevents false positives in auth monitoring.

Suggested Agent: MCP integration agent

Estimated Effort: Quick (< 1 hour)

Data Source: DeepReport Intelligence Briefing 2026-01-20; discussion #10821 (run §21170454994).

AI generated by DeepReport - Intelligence Gathering Agent

[github-actions]

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