We have also been updating the iPad version of the app with the new Modern format, deck filtering and legality search, as well as paging through searched. We also managed to squeeze in a turn counter into the upper right corner of the test deck section. Tapping the turn counter would both draw a card and increment the turn, thereby saving you a tap.
All the development is nearing completion, and we hope to roll out the changes next week if no further bugs pop up.
Check out the screenshots below.