Describe the bug:
After editing a visualization that uses the state transfer service to navigate to an editor + back to dashboard, unsaved changes gets stuck on the Dashboard. Possibly related to #188039, since we changed some logic for handling the incomingEmbeddable in that PR.

Steps to reproduce:

1. Add a map to a dashboard (or any other embeddable that does not have inline editing + uses the state transfer service)
2. Save the dashboard
3. Edit the embeddable from step 1
4. Make some changes, then click "Save and return"
5. Your dashboard has unsaved changes - this is expected
6. Try to save your dashboard - unsaved changes does not go away 🔥

Expected behavior:
Unsaved changes should go away.

Screenshots (if relevant):