fix: avoid warning for Bing home page

[zhangMonday]

Summary

• Avoid reporting the normal Bing home page as an unknown login state.
• Prevent unnecessary unknown-page diagnostics during successful Bing session verification.

Root cause

verifyBingSession() called the generic login-state detection before checking whether the browser had already reached www.bing.com/.

The normal Bing home page does not contain the login-page selectors used by detectCurrentState(), so it was reported as UNKNOWN. The same loop then correctly recognized the Bing home page and verified the session successfully.

This caused a misleading warning:

Unknown state at www.bing.com/, waiting

Changes

• Check whether the current page is the Bing home page before running generic login-state detection.
• Continue handling password, Passkey, and other login states on non-home pages.
• Keep the existing Bing session verification behavior unchanged.

Testing

• Verified the issue using the reported login logs.
• Confirmed that the normal Bing home page no longer enters the UNKNOWN state handler.
• Confirmed that non-home login pages still use the existing state detection flow.