Most of the issues noted are because of the wide angle lens of the iPhone. The more expensive iPhones (the Pro models) have 3 lenses one of which can produce photos similar to a traditional camera.
There are three different lenses on the iPhone 16 Pro. Which one gets used is determined by the "zoom" level you pick. The "0.5x" picks the widest angle lens, the "1x" and "2x" use the same lens, and the "5x" uses the third lens.
If you wish to reduce optical distortion and can get farther away from the subject, you'll want to pick the "5x" zoom. Think somebody else here said it was a 105mm equivalent, which sounds about right.
Intermediate values are obviously crops... although given that the 0.5x and the 1x lens are both 48mp sensors (IIRC), and the resulting image is typically 12mp, it doesn't make as big of a quality difference as one might ordinarily think.
It appears the long lens on that phone is 120mm-equivalent ("5x") and any intermediate zoom is just cropping. A 2x "zoom" (crop) would get pretty close to the field of view of the author's dedicated camera lens, but with further reduced image quality.
Actually using the iPhone telephoto for a group photo like the one shown in the article would require the photographer to stand a considerable distance from the subjects, and then we might start noticing a little perspective distortion from the 45mm-equivalent lens on the Sony.
For mid to long ranges, a dedicated camera with A Big Lens is still the way to go, but for wide angle and landscapes the better iphone cameras are very competitive.
For 28 Years Later, note that while the iPhone sensor did in fact ultimately collect the photons for the movie, they attached substantial professional-grade glass to the front to augment the phone camera.
My understanding is that all that extra gear is mainly to enable more ergonomic manual control for things like focus. The matte box and ND filter are probably the biggest boosts to image and motion quality, and there are affordable ways to get those on your phone.