Breadcrumbs

The actual breadcrumb view is not in SpringBoard or its' UIStatusBar. It is inside the application. It is inside UIStatusBarForegroundView and then inside a UIStatusBarBreadcrumbItemView.

The action is stored in the UIApplication (NOT SpringBoard!) [[%c(UIApplication) sharedApplication] _systemNavigationAction]

Disabling

1. Hook UIKit's UIStatusBarForegroundStyleAttributes, and override canShowBreadcrumbs and its associated setter method
2. Return NO for SBMainDisplaySceneManager's - (_Bool)_shouldBreadcrumbApplication:(SBWorkspaceApplication *)arg1 withTransitionContext:(id)arg2;

Resources

1. Homemade Bread - an open source tweak that allows you to use the home button to activate a breadcrumb