I am having similar issues being able to login programmatically whilst using @nextjs-auth0 and Cypress. I have been able to login via the UI using Cypress but this is far from ideal considering the volume of E2E testing I want to do and having to be redirected to an Auth0 login screen, while automated, is still time consuming.
I raised this post yesterday and am close but I am struggling to store the appSession cookie correctly which is causing all subsequent requests to be returned with a 401. Link to my post here.