After sign-in, and from the Auth0 logs we can see that the sign-in itself is successful, a redirect loop begins, cycling through the callback (index.php?auth0=) > wp-login.php > authorize (at the Auth0 tenant).
The Auth0 logs show no errors, nor do the Wordpress logs. Someone else had this same issue in 2019 (link below), but as often happens, they never followed up or posted a solution. We have generated the HAR file if there is someone from Auth0 who could have a look for me.
Thank-you for your help - you pointed us in the right direction. One of our own plugins forced sign-in across the whole site and this was causing the loop.