What we can do with Cross App SSO

I’d like to get a clear understanding of how Cross App SSO can be used.

I have two applications.
They must be separated completely, meaning that they cannot share the same top-level domain.
The Database can be shared.

e.g,
App1 : https://app1.com
App2 : https://app2.com

①Assume the user had App1 and App2 open simultaneously in one browser.
②Next, the user clicks the login button in App1 and authenticates with App1 via Universal Login.
③In that state, if the user refreshes the page of App2, the user automatically logged into App2.

The above scenario is the use case I have envisaged.
Is it possible with Auth0?

Through trial and error, I’ve found that the following behavior seems achievable.
①② same as described above.
③The user clicks the login button in App2, then the user can logged into App2 without Universal Login.

Is this the limit of what we can achieve with Auth0?

I’ve found the solution.
When accessing a page with Root Guard without authentication, the user will be redirected to the Universal Login screen.

So I made a global middleware like this.

import { useAuth0, authGuard } from "@auth0/auth0-vue";
import type { RouteLocationNormalized } from "vue-router";

export default async function (to: RouteLocationNormalized) {
  const auth0 = useAuth0();
  const { isAuthenticated, isLoading } = auth0;

  // watch the loading flag
  Object.defineProperty(isLoading, "_value", {
    set: async (): Promise<void | boolean> => {
      if (isAuthenticated.value) {
        // get JWT token here
      } else {
        if (to.path !== "/login") {
          return await authGuard(to);
        }
      }
    },
  });
}

I’m using Nuxt3 and Vue SDK.
Since the official Nuxt SDK is not available, I’m not sure if this is the correct approach.

Is there a better way?