The circle you’ve drawn does not split the larger face as evidenced by the heavy profile edges and the addition face inside the circle. I deleted it and redrew it after which Push/Pull worked as expected.
I can’t tell what you did when you drew the circle, though.
Something is different when you draw the circle. See what happens if you make the circle with a radius of 9.5 instead of 10. If you can push the face through, select the edge and edit the radius to 10 in Entity Info. Do the same for the opposte end of the hole.
SketchUp is quite confused about how many faces are associated with that circle. When you drew it, you may have somehow triggered a bug similar to the notorious “bow-tie” bug. In any case, erasing it and redrawing it carefully forces SketchUp to rethink the situation and heal the problem.
I did notice you have some garbage geometry under the horizontal face. Maybe if you get rid of that you’ll have different results when you draw the circle for the hole. I wonder why you used the Circle tool to make that lobe in the first place. The 2-Point Arc tool would have been a better choice.
The stray arc @DaveR observed is indeed a problem. I also just discovered that to force SketchUp to repair the confused circle, it is sufficient to redraw any of its edges using the line tool.