The Gemini CLI supports OAuth login via `gemini auth login` which stores
credentials locally without setting any env vars. The previous warn-level
check on missing GEMINI_API_KEY caused false alarms when CLI-based OAuth
was used. The hello probe that follows is the real auth authority — if
auth is actually broken, it will catch it and report appropriately.
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
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