> I don't have access to the paper

https://arxiv.org/abs/2306.04053

Someone usually posts up a preprint in discussions where the original link is a summary put out by one of the authors' institutions' public relations department and published unchanged or made even worse by some aggregator site's editing.

You can also install the Unpaywall extension which gives you a one-click button to (usually preprints of) a large proportion of freshly published papers (it works on more than half of astrophysics-related papers). http://unpaywall.org/ is one of the best things on the Internet.

> it would probably be beyond me

That's OK, it's also clearly totally beyond the author of the article reproduced at "advancedsciencenews".

You are correct to be puzzled about the lack of "redshift" appearing in the article; "high-redshift" is literally the eighth word in the title at Nature, and "redshift-dependent time dilation" appears in the first sentence of the abstract.

The first sentence of the Introduction (in preprint) reads, "A fundamental consequence of the relativistic picture of expanding space is cosmological time dilation, where events in the distant universe appear to move slowly compared to those in the local cosmos." Emphasis mine.

That's correct and totally conventional.

The first sentence of the "advancedsciencenews" article reads, "Scientists have confirmed that just 1.5 billion years after the Big Bang, time ran five times slower than it does today, 13.8 billion years later". I count several errors there, and struggle to see how a mere broken-telephone effect arrived at that wording.

1.5 billion years after the big bang, atomic electron transitions (like the n = 2 orbital to n = 1 ground state transition in atomic hydrogen) happened at the same ~nanosecond speed as 13.8 billion years after the big bang, emitting the same frequency photon (2.47 PHz) at both times. That transition speed and photon-frequency-at-emission each forms a sort of a local clock (or really frequency standard) which has travelled along from well before 1.5 billion years, through that 1.5 billion year mark, to the current age of the universe. We can test them tomorrow. We can test them next week. We can test them on the Moon or in more distant spacecraft. The ~nanoseconds transition and more precisely the emitted-photon frequency are always and everywhere the same when measuring locally, i.e. very near the emission and not moving quickly with respect to it.

General relativity tells us that, when there is significant gravitation or expansion of space, when we look at distant clocks (or really frequency standards) they appear to tick at different rates than clocks local to us. In particular, clocks in the distant past of an expanding universe appear to tick slower than clocks in the less distant past (and those tick slower than clocks here-and-now).
(Special relativity tells us that when we look at clocks that are in motion relative to a clock we have locally, the "moving" clock appears to tick slower.)

Consequently, the photon of an n=2 -> n=1 atomic hydrogen electron transition in the early universe will in the present universe have a frequency lower than 2.47 PHz. If we get to watch a transition happen (we can't, they're too small to see at great distances, but we can see the speed reflected in the bulk behaviour of atomic hydrogen gas lit by bright sources like ... quasars!) we'd see it happening slower. And from this we have the first line of the actual paper.

Additionally, hopefully shedding further light, we could drop in someone who is half way between 1.5 billion years and the present age of the universe, and locally they'd measure the same local ~nanosecond transition and the same 2.47 PHz photon frequency. Looking at the same 1.5 billion year universe source, the intermediate observer will also see a redshifted photon-frequency and a slower transition, but not as slow as we see even more billions of years later. In general, observers of the same source who are ever closer in time to that source will see a photon frequency and atomic electron transition speed ever closer to what they measure locally; whereas later observers will see an ever-greater difference (the later the observer the redder (slower transition, lower frequency) the ultimate observation).

The "appear" in the Nature article's first sentence deserves my italicization. It's important. And it seems to have not been noticed by the author of the advancedsciencenews summary. And it's clearly confused many people here. Hopefully with this comment I can unconfuse at least one person, at least a little.

Finally, the paper is about showing that variable quasars have an intrinsic set of luminosity-variation statistics, and intrinsic means that those statistics are local to the quasar. We should then see those statistics change when redshift changes. And that's what the authors show: the "intrinsic brightness-change-rate statistics" appear to generate slower brighness-variations for quasars that are at higher redshifts (measured by other means including the redshifting of absorption and emission spectral lines caused by the quasar's light passing through atomic hydrogen for example, and including the apparent area on the sky and brightness of the quasar's host galaxy).