/doctor flags "1 setup issue: chrome" on Chrome Beta-only machine while extension is connected and fully working

Environment: Claude Code 2.1.173, Windows 11 Pro

Summary
On a machine with only Google Chrome Beta installed (no stable Chrome), every session shows !! 1 setup issue: chrome - /doctor even though the Claude in Chrome integration is fully functional. Restarting never clears it.

Verified healthy while the warning shows:

• Extension connected (list_connected_browsers returns the local browser; all automation tools work)
• Native host registered at HKCU\Software\Google\Chrome\NativeMessagingHosts\com.anthropic.claude_code_browser_extension
• Manifest at %APPDATA%\Claude Code\ChromeNativeHost\com.anthropic.claude_code_browser_extension.json is valid; chrome-native-host.bat present under ~/.claude/chrome/

Not present: stable Chrome. Only C:\Program Files\Google Chrome Beta\ exists (no C:\Program Files\Google\Chrome or %LOCALAPPDATA%\Google\Chrome).

Expected: the doctor chrome check should treat any Chrome channel (Beta/Dev/Canary) as a valid install. All channels read the same NativeMessagingHosts registry key on Windows, and the integration demonstrably works from Beta.

Actual: the check appears to probe stable Chrome install paths only, so the banner fires on every startup and cannot be cleared.

Side note: there is no way to export the /doctor report to identify the exact failing sub-check (claude doctor has no flags). Happy to provide more detail.