Why is the first answer a machine polisher? An agressive and non-diminishing compound?? And all this on a leased car???
The first step is for the OP to read up on deatialing, waxing and how clearcoats work. The term "paint correction" is highly missleading, it should be "paint reduction" as in
"I am going to reduce my clearcoat thickness by 10% to remove surface hazing."
Once that's out of the way, the main question is if anything needs to be done. That can't be evaluated except by giving the car a good washing, using a prewax cleaner to deep clean the paint and claying.
At this point the paint surface is fully clean, and you can evaluate it. Truely fine surface hazing should generally be ignored, because the wax or (wax + glaze) will hide it. Hazing that is visible head on, is much more of an issue than hazing which can only be seen in angled light.
Any visible scratches that are noticeable should be polished with a goal of reducing the sharpness/distinctiveness of the scratch's edges. A bottle of Kit scratch out, and a few foam pads are all you need for this.
After that apply some cleaner wax, have a beer, and then re-evaluate the paint's condition.