I'm unable to figure out automating an embedded browser on Mac, though we have done it for a Windows/CEF combination.
Check if Squish tool can help you.
Squish is GUI automation framework they support macOS application with embedded WebKit.
Sikuli can be an option:
Sikuli automates anything you see on the screen. It uses image recognition to identify and control GUI components. It is useful when there is no easy access to a GUI's internal or source code.