I'd say that, if the new Z is still in the 4 second range (particularly with an automatic), Nissan will have failed. To produce a vehicle - a sports car - that is only marginally quicker than its 13-year-old predecessor would be somewhat embarrassing.
Again, the Q60 can reach 60 MPH in 4.4 seconds according to Car and Driver and it weighs almost two tons. Supposing the Z gains a little weight, I'd still place it around 3,400 lbs. If they can't make that engine perform more impressively in a far lighter vehicle, they didn't try very hard, in my opinion.
For 2WD cars I tend to disregard the 0-60 claims. Oftentimes, the 0-60 performance is equally reliant on chassis dynamics. With the new Z being significantly more powerful (if 400HP minimum is what we get), and the same weight as the 370, I suspect 0-60 times won't be wildly different. I do believe a turbo Z will absolutely get out in front of a 370z with no doubt as to who is winning, but traction will be the issue. I prefer to look at 1/4 mile trap speeds. Much like how a Dodge Challenger Scat Pack Widebody can keep up, if not out-accelerate a Hellcat on the street, the Hellcat will eventually run away from the 392 Scat.
Going by well established stats, the quickest I have ever seen a 370Z 7AT trap in a 1/4 is 108mph. I have consistently seen Q60 RS 7AT do 111mph. Rough rule of thumb is each 1mph at the end of a 1/4 looks like a full car length, roughly. So, a Q60 is 3 cars ahead of a 370Z 7AT at the end of a 1/4. Whilst carrying several hundred pounds more weight.
My older 3.7 7AT Q60 (it's technically a G37, but in 2014 Infiniti got weird with the names) can only get through a 1/4 at 104mph. So, the sister 370Z 7AT is 4 mph faster than it's exact Q60/G37 sister. This should translate well to the new Z as the current Q60, my older Q60 and the 370Z and new Z will all have about the same relative weights for the most part.
If we apply that exact same delta to the new turbo Z, plus account for the extra power, it would be fair to say that the new turbo Z could easily be +5mph faster than the current Q60, if the new Z uses a 7AT. That would put it trapping 116mph, only 1mph behind a BMW Supra. However, if Nissan gives us an amazing automatic trans, we could see even another 1-2mph gain from a better trans. So, it is quite feasible a new turbo Z could run neck-and-neck with a BMW Supra.
But, it doesn't matter to me one bit. I would never cross-shop a BMW with a Japanese car. My current considerations for my money are:
Supercharge my Q60 (this is the cheapest option by a long shot)
2022 BRZ (I know, not a HP monster, but it is a very compelling Japanese RWD coupe)
new TLX Turbo V6
new Turbo Z
And all of the aforementioned choices are with full knowledge that an upper-level AWD Tesla could whoop up on any of those choices. Can easily whoop the snot out of a BMW Supra too!