I thought they already measured this via satellites and time dilation, GPS in particular has to know exactly how much time is lost
The team here measured the gravitational redshift by comparing the clock-rates inferred from atoms at the top and bottom of a cloud of atoms that was itself smaller than a grain of rice.
I've spent much of my career building precision gravity-sensing systems -- I'm happy to assure you that this news is very cool. Clocks are an awesome way to learn a lot of new things about gravity, particularly because they measure differences in potential, rather than differences in acceleration. In the past two decades, we have seen atomic clocks begin to become sensitive to terrestrial gravity. In the next two decades, we are likely to see clocks begin to open up previously-impossible measurements.
The measurement described here is a wonderful stepping-stone on that path.
800 nanokelvins down to 100 nK! Brrr! [https://arxiv.org/abs/2109.12238 "Atomic sample preparation", pdf p. 16, and top of p. 3]
Maybe it's soon time to plan updates to PARCS/ACES/SAGAS.
To your point, maybe, I wonder if they had to factor in the relative velocity difference of the top and bottom of the cloud due to the rotation of the earth at their latitude (or just do the experiment at the south pole). At the equator, assuming a cloud of 1mm diameter, it would be 2π mm/day, which according to a sloppy google search is 2.425675e-16c.
It could be that time dilation is caused by some underlying physical system having a bottleneck, thus causing the slowdown. The underlying physical system has to evaluate all possible states for a particle in superposition, even if working in parallel. Then i would guess a particle in superposition should always experience the biggest possible slowdown.