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When multiple OAuth providers share an account email, the existing "Use OAuth" debug lines are ambiguous and hard to correlate with management usage stats. Include provider, auth file, and auth index in the selection log, and only compute these fields when debug logging is enabled to avoid impacting normal request performance. Before: [debug] Use OAuth user@example.com for model gemini-3-flash-preview [debug] Use OAuth user@example.com (project-1234) for model gemini-3-flash-preview After: [debug] Use OAuth provider=antigravity auth_file=antigravity-user_example_com.json auth_index=1a2b3c4d5e6f7788 account="user@example.com" for model gemini-3-flash-preview [debug] Use OAuth provider=gemini-cli auth_file=gemini-user@example.com-project-1234.json auth_index=99aabbccddeeff00 account="user@example.com (project-1234)" for model gemini-3-flash-preview