Just completed testing Tire Registration function. Did it three times. Twice with 0.28.13 and then again taking out the quick fix to 0.28.13 (basically back to 0.28.12) that was not needed and did nothing. Below is a screenshot after a successful registration. The first number under the start button changes from "0" to "f0" when it is successful. If it stays zero it failed. The second number changes to "1" while the registration is in process and changes to "2" when it is successful. It will go to "4" if it fails.
The step numbers (to the right of the Connected message) should cycle between 92,93,94 while the registration is in process. If not then let me know as that should not happen. Those three steps request tire registration status (the two number below button), tire registration numbers and the tire pressures. It should stay in that loop until status indicates completion (good or bad).
So bottom line is I don't see any issue with either 0.28.12 or 0.28.13.
Before you started tire registration do you recall what tire pressures the app reported? Were they similar to what you see on the second screenshot (order is probably different or you would not be doing a tire registration)?
Note that after a successful registration the tire warning light will come back on because the rear left tire is too low. You will also get a message to check tire pressure.