It's not the fan, it's the box that matters. To handle the load of a ceiling fan, the box needs to be securely mounted on 2 sides. This is accomplished either by boxing it (using 2x4's attached between studs, making a box), or installing a ceiling fan box that has extendable legs...before sheetrock is installed.

The ceiling fan box can be retrofitted, but it's not easy.

You could try a ceiling fan mount adapter, but if your current box is mounted to the side of a ceiling joist, the opening in the sheetrock won't line up.

Edit: all this said, I've found rental managers are oblivious, and have changed all sorts of things that they never notice. But, I've worked on houses since I was a kid, worked for general contractors, plumbers, HVAC guys, carpenters, etc, so I know how to do just about anything. I'd have no problem installing that metal leg box, and repair the sheetrock as needed. It's not hard, just a little tedious.

Can lights are held in place by spring clips.

You can just tug them down and unclip the wire, then poke a camera up the hole to peek at the studs.

I think can light housings usually are not attached to studs.