Why diameter does so much
A shaft’s resistance to bending rises very steeply with its diameter, not in proportion to it. Strength Shop put it well on the Riot Squat Bar listing: a thicker shaft is inherently stiffer, and that stiffness increases steeply with diameter, so the extra millimetres over a power bar make a large difference.
In practice, at weights where a 29mm power bar starts to oscillate on your back as you stand, a 32mm or 35mm bar does not. That is worth a great deal when you are under it.
25kg, and the plate maths
Squat bars weigh 25kg, not 20kg. Every time you work out a load you need to remember it, and if you are following a programme written around a 20kg bar you are lifting 5kg more than it says.
They are also longer: Rogue’s 32mm bar is 2400mm, Mirafit’s Leviathan is 2400mm, the Riot 35mm is 2300mm. Check your rack width and the room either side.
Fully knurled, usually
Most squat bars are knurled along their whole length, with a centre knurl and often orientation rings so you can find the middle by feel. The reasoning is simple: nothing should move. Your hands do not slide, the bar does not slide on your back.
It does mean the bar is unpleasant to do anything else with, and that is fine, because you should not be doing anything else with it.