How to reload one site from another while maintaining SSO/SLO across browser tabs?

Question

I am implementing an SSO (Single Sign-On) and SLO (Single Logout) system where two different sites need to maintain synchronized session states. Both sites run in the same browser but in different tabs.

Here’s the scenario:

When the session changes (e.g., logout or login) on Site A, Site B needs to automatically reload or update its state.
Both sites use the same identity provider (IdP) for authentication.

Using localStorage or sessionStorage for inter-tab communication, but it seems inaccessible across domains.