1. Click on the 'Speechify' plugin at the top right of your browser again. Log in with your credentials.
2. It should take you to a sign-in page → on this page click on Continue with Apple and log in with your registered Apple ID
3. You should then be able to use the extension on your premium subscription.
4. To sign out, click on the 'Settings' icon, and click on 'Show All Settings'.
5. On the lower-left-hand corner, click on Sign out.