Hello,
I have the same problem with crop tool (in fact with most tools). I have just installed Affinity Photo (v. 1.9.2) on a new Mac Mini M1. I open a photo click on the crop tool and move over to the image. But, as soon as I get the image 'window' the crop tool icon changes to the hand icon and as I move the image moves. The same thing happens with many of the tools. I suspect this is a Big Sur compatibility issue. I am trying Affinity only because Lightroom and Photoshop also have issues of compatibility with Big Sur.
So generally I am not a happy bunny having just invested in the new mac and its new OS.