In time the web app will mirror the functionality of the mobile app, but for now you're right that withdrawing rewards needs to happen on the mobile app.

If you sign-up to the web app with an email/password, then you can access the mobile app with the same credentials. You can also connect LNURL Auth to an email/password account via the web app currently. LNURL Auth is indeed coming to the mobile app too, which will close this loop entirely so you can login to both using only LN Auth if you prefer!