Summary

• Stabilize breadcrumbs badges append extension content identity so unrelated extension updates do not recreate the badges mount function.
• Refactor badges stream derivation into small helpers to keep the state pipeline easier to reason about while preserving behavior.
• Add focused unit tests for createBreadcrumbsState identity behavior on non-badge extension updates, badge updates, and isFirst transitions.

Test plan

• yarn test:jest src/core/packages/chrome/browser-internal/src/state/breadcrumbs_state.test.ts