Thank you for your response.
Yes, that is correct. Auth0 SSO is dependent on browser cookies.
AFAIK, by default, Microsoft Edge does support cookies. But, circling back to your original question:
It will not be possible to achieve SSO across different browsers. You could verify this behavior as well by testing this on your local machine.
Once you log in to your Dashboard using Google Chrome, that cookie will reside within Google Chrome itself. Accessing Microsoft Edge or any other browser will not be aware of the authentication session (stored as a cookie) since that information is browser-dependent. That is, only Google Chrome has information stored about the authenticated user’s session.
For Microsoft Edge or any other browser to be aware, the user must re-enter their credentials to log in. Doing so creates a cookie within Microsoft Edge.
The canonical way SSO works is within a single web browser. For example, if you are already authenticated on Gmail using Google Chrome, then there is no need to log into Youtube or any other Google services.
Hoped this helps! Please let me know if there are any questions.