Conclusion:

The new wider Z-mount with its shorter register means there’s a lot more flexibility for optical engineers when designing lenses. The mount should especially benefit wide-angle lenses, and indeed, the Nikon Z 35mm f/1.8 S is the highest-scoring Nikon 35mm lens we’ve tested to date. Its key strength is sharpness, with good performance at the maximum aperture and exceptionally uniform resolution at the mid-apertures. This said, it doesn’t quite match such third-party options as the Sigma 35mm f/1.4 A and the Tamron SP 35mm f/1.8 Di, which achieve better sharpness when tested on the lower-resolution 36.3Mp Nikon D800E, compared to the Nikkor Z lens on the 45.7Mp Nikon Z 7. Overall, however, Nikon Z-system shooters who are looking for a 35mm prime can rest assured that the native Nikon Z 35mm f/1.8 S lens is an optically excellent choice.

The Nikkor Z 24-70mm F/4 S has been tested at DxOmark:

When Nikon announced the new wider Z-mount with a short flange back, the prevailing thought was that there would be a real leap in image quality. The Nikkor Z 24-70mm F/4S is without doubt an attractive addition—it is, after all, a very compact and user-friendly lens—but the best way to describe its optical performance (at least on the high-resolution Z 7) is “well-rounded.” It admittedly brings unprecedented uniformity to a zoom—there’s no measurable astigmatism—but that appears to come at the price of outright resolution. There’s also no denying it has excellent transmission, but unless you’re into serious film-making, that isn’t going to be high on your wish-list. Bought separately, it’s also not what we would call inexpensive, especially without OIS. But when purchased as part of a kit, it’s an entirely different proposition and well worth taking a closer look.