Safari: Google won't stay logged in

The built-in Google search stays logged out no matter what I do, interrupting me with a sign-in pop-up every time I search for anything.

This was a persistent problem on my previous phone and remains on my new iPhone 16 Pro Max with iOS 18.

Yes, I've done all of the following:

• Ensured cross-site tracking is enabled in Privacy & Settings
• Ensured cookies are enabled every time in Privacy & Settings
• Restarted Safari (multiple times)
• Restarted the phone (multiple times)
• Updated to the latest version of iOS (multiple times)
• Disabled all ad blockers.