Try increasing it to like half the capsule radius. Is not explained well anywhere, but with 0 it seems that you only need 0cm of base on floor to perch. Is kinda counterintuitive.
Here’s my 2.5 d char standing on ledge with perch radius of 0:
and 30:
I unticked “can walk off ledges” before screens, so that’s the absolute limit. Also changed cam to ortho to make it clearer.