Describe the bug:
Adding any React embeddable to the dashboard results in unsaved changes that do not go away until either "Reset" is clicked or the dashboard is reloaded. Possibly caused by the same underlying issue as #190065, but creating a separate issue just in case they are unrelated.

Steps to reproduce:

1. Add any React embeddable to the dashboard via the "Add panel" menu (Maps, Links, Image, etc.)
2. Try to save your dashboard
3. Unsaved changes do not get cleared 🔥

Expected behavior:
Unsaved changes should go away.

Screenshots (if relevant):