About twice a year I search high and low for shorts with side pockets that are 5" or less…and find nothing. There are brands with shorts that are identical in style at 9", 7", 5", & 3"…except only the 9" & 7" have pockets. But unless we're talking about split shorts, there is nothing about a 5" or 3" short that cannot support side pockets, when the same style in a longer length can.

Anyway, this time around, I have found a couple of possibilities.
One is from BALEAF, a nylon v-notch 3" running short with zippered side pockets, which I have ordered—no reviews on Amazon, so I'm assuming it's a new style. https://www.amazon.com/gp/product/B091HW85TR/

The other are "pocket silkies" from Sunga Life. Basically, 2-in-1 silkies with phone pockets in the compression liner. Overpriced, and mostly hedious patterns, though. https://www.sungalife.com/collections/pocket-silkies/