Dark triangle on shadow edge (cycle mode only) I just place the Zuzanne's head on the center,  a light, and a camera.
In cycle render mode, I got some small dark triangle on the shadow edge.
In Eevee render mode, Everything is ok.
It seems not a z-fighting, face orientation is OK.
Material is not related to this. I tried to remove all material, triangle is still there.
It is a simple scene.
Did I do anything wrong?
Try to increase Suzanne's Subdivision levels with Subsurface Modifier.
Try to increase Lamp Angle.
Or you can increase Shadow Terminator Offset for smoother shadow transitions.
Image below: Shadow Terminator offset 0.00 vs 0.1: