How much better is this workout than my PR?

Yeah, it's safe to say you are in better shape than your 4 mi pr. How much better? Depends. Likely somewhere between 27 - 28. For those minutes, any idea what was hard pace, what was easy pace? What was the effort level of the workout? In any case, I'm not sure you'll be able to hit that half goal on only 20 mpw. Say you're in 27:45 shape for 4 mi, that equates to approx a 1:39 half given adequate training for each. I'm not sure you have the endurance on 20 mpw to get there. You might, especially if you're still improving (or if you're in better shape for the 4 mi than 27:45) but it's no lock. If you can bump up the mileage carefully with some extra very very easy miles to 25-35 mpw, I think it's a sure thing.

After the half, if you really want to bring your times down, run more mileage. Do it carefully. Do lots of easy running with occasional strides, one short tempo run a week (not too fast!). Learn to listen to your body, train smart, and you have a lot of room to improve. Good luck.

20 mpw? Up the mileage. You know that already of course, but what you don't know is how to do it safely. It's easy, just slow down at the beginning and pick it up towards the end.