@jelarv Some possible contributors:
1. New tire grease is very real in my experience! If these are brand new tires with just a handful of miles, do NOT try to hoon around in them right away, and don't judge their grip immediately. Wear through the manufacturing grease first. A couple hundred miles should do it, maybe less I'm not really sure. But 10 miles, for example, was NOT enough to wear off that grease last time I tried pushing brand new tires hard!
2. Check your tire pressures. Did the shop overflate them higher than you were using before? Overinflation will reduce traction. For some reason tire shops always want to overinflate my M3P to 45 PSI cold even though the door sticker says 42 PSI cold - and I think even 42 PSI is too high for best traction, 40 PSI cold or even
slightly less feels better, depending on the tire. (Then again, since you're still on stock 20" sizing I'd be very cautious about potentially under inflating. Probably best to stick with 42 PSI cold exactly in that size. I'm on 245/45R18 now so I have less risk of rim damage or pinch flats than with the stock 235/35R20 rubberbands.)
3. As you can see from this thread...a majority of us feel the PZ4 just aren't very good for the category. I haven't used the PS4S myself, but I can say the Bridgestone Potenza Sport easily outgripped the PZ4, dry and wet. I don't doubt the PS4S does as well, so it's possible you're used to a better performing tire.
That said the PZ4 did generally feel like a performance tire, just not a particularly good one. If your grip levels feel so bad it's like driving on MXM4 eco garbage, then there's probably other factors involved (e.g. points 1 and/or 2) besides the PZ4 being mediocre for its category.