I received the speed controller did some testing. Based on some other fans with a built-in speed controller I've tested in the past, unless I'm misremembering them having PWM, I'm starting to think this fan may be PWM compatible.
I found that if I didn't have the dial up to around 60% minimum, that the fan would only spin temporarily, spin back down, then spin back up, and keep repeating that, which is what I have seen when I didn't turn up other fans I've tried in the past that has speed controllers.
Maybe that minimum speed is okay, it seemed kind of high, but it has to push through cushion, so I'm not sure if that range was acceptable or not, probably could live with it.
I decided to do some testing of the voltage through the speed controller to see if voltage was being adjusted. At around that 60% setting, it was still running at 12 volts. I even turned it all the way down to the very lowest setting which doesn't even run the fan at all, yet it was still delivering 12 volts, so unless you can't test the voltage properly through the speed controller, which I would think you could, then it doesn't seem to be adjusting the voltage, yet it does change the fan speed.
A related thing I found was that if I clicked it all the way off, the voltage dropped to zero, so it seems like it is able to be used as an off switch since in the opposition there is no voltage coming through it anymore.
Edit:
I did misremember PWM in the other fans I tested, not that I know they didn't use it, I'm just not sure. The one specifically says that it adjusts the voltage to control the fan speed. Here were the two different fans that I had tested.
Wathai 120mm x 38mm 110V 220V AC Powered Axial Fan ,12V Variable Speed Controller with AC Plug ,for Receiver Xbox DVR Playstation Component Electronics Cooling and Cabinet Ventilation
https://a.co/d/2ZRGmSn
AC Infinity AXIAL S1238D, Dual 120mm Muffin Fan with Speed Controller, UL-Certified for Doorway, Room to Room, Wood Stove, Fireplace, Circulation Projects
https://a.co/d/9BdCwhy