Rather depends upon what you consider "long" to mean. The sun moves about 15 degrees per hour and the angular field of view on a zoomed iPhone 13 shot is about 23 degrees (according to a blog). 12MP resolution so crudely moves about one pixel per second. A ten second exposure is certainly long compared to the light gathering drive by the eye, but a ten pixel elongation of the blob of a bright star won't be very obvious, may be rather less than the smearing caused by atmospheric "seeing"

Whoa, you're just way off base here. You can take a long exposure and avoid star trails depending on a couple of factors, primarily the focal length of the lens. The longer the lens, the less time it takes to start seeing trails. The wider the lens, the longer you can take. I've taken up to 45s exposures with a 20mm lens on a DSLR with no trails. Since most lenses on camera phones are typically wider angle, the limiting factor is having a support to hold it for longer exposures.

Some sources (https://lweb.cfa.harvard.edu/webscope/activities/pdfs/eyeTel..., page 7) say the human eye's "exposure time" is around 1/15th of a second. So a 1 second exposure is 15 times longer and won't see star trails, at least not at normal zoom levels.

You absolutely see star trails on iphone night mode photos when setting exposure to 10s or more. For aurora, 10s is way too much though, 1-3s seems right and is what the iphone allows to do when not on a stable surface or tripod.