The issue you’re seeing (as pointed out in the thread you mention) is that third-party cookies are being blocked in Safari (thanks to its ITP technology), and you will find the same thing in other browsers that also block third-party cookies (such as Brave, with its shields up). While not a tracking cookie, Auth0 still relies on the ability to transmit this cookie in order to perform silent reauthentication.
This is mostly with us to find another way to allow silent reauthentication without using this cookie. We currently have a beta release of the SDK that would allow you to use local storage to keep your access token for longer (surviving page refreshes), although it doesn’t solve the whole problem as it depends on the expiry of your access tokens. We have more advancements in this area coming too.
Primary release notes for the beta are here: Release v1.7.0-beta.1 · auth0/auth0-spa-js · GitHub
It can be installed using npm install @auth0/auth0-spa-js@beta.