Screencast software integrates with Fusion, and will show us your mouse clicks and other Fusion mechanisms.
After you draw the circle, turn off the body that contains your arc.(Eyeball)
There now you see why you can’t use it, there is nothing else in your sketch, to snap to.
So it’s Create Sketch,
Use create > Project > Project, Select the arc, it will supply a purple arc to use. Hit Ok.
Hide the orange body, with the body eyeball.
Draw circle, the centre point will snap to the purple line,
Show the orange body.
Extrude > Cut shows a red preview, this expected behaviour, and not an error, now that you have the purple arc, you will also cut the circle profile into two parts. Again expected behaviour, you will have to select both to cut a circle.
Now - Cutting a Slot for clamping has nothing to do with your side on activity.
Create a sketch on an Offset Plane above or below the clamp,
draw an appropriate slot,
Extrude cut the slot through the bracket. Down or up through in the vertical direction.
Might help....