Do I need to configure Google Cloud Console when using "Managed by Lovable" setup?

No, with Lovable-managed Google authentication, Lovable handles the Google Cloud Console setup for you. You don't need to create an OAuth app or manage credentials yourself. If you choose to use your own credentials instead, then you'll need to set up a project in Google Cloud Console, create OAuth credentials, and provide the Client ID and Secret to Supabase.