/doctor reports unconnected claude.ai account connectors as "needs authentication" issues (false positive)

What happened

/doctor lists every available claude.ai account connector that isn't authenticated as a health issue, with a suggested fix to run /mcp and authenticate:

- MCP server 'claude.ai Google Calendar': needs authentication
  Run /mcp to authenticate, retry, or inspect the server.
- MCP server 'claude.ai Gmail': needs authentication
  Run /mcp to authenticate, retry, or inspect the server.

These connectors are deliberately not connected. On claude.ai → Customize → Connectors they correctly appear under "Not connected" (only Google Drive is connected). Nothing is misconfigured.

Why it's a bug

/doctor conflates two different states:

1. A genuinely broken/actionable problem.
2. An available-but-intentionally-unconnected account connector — working as designed, no action needed.

Reporting #2 as an issue with a "Run /mcp to authenticate" fix is a false positive. It nudges users to connect services they've chosen not to use, and there's no way to clear the warning: the connector is account-catalog-managed (Scope: claude.ai config), and claude mcp remove "…" -s claudeai fails with Cannot remove MCP server from scope: claudeai. So the warning is permanent and unsuppressable.

Expected

Unconnected, never-authenticated account connectors should not be reported as /doctor issues — either omit them, or list them as informational ("available, not connected") distinct from actionable problems. An authenticated-then-broken connector is a real issue; one that was never connected is not.

Environment

• Claude Code 2.x (native install, ~/.local/bin/claude), macOS (Darwin 25.5.0)