Can't subtract front shape

Could you please post screenshots taken at View > 100% with the pertinent Panels (Toolbar, Layers, Options Bar, Paths, …) visible? 

"I tried putting the shapes on two different layers and the same thing happens. "

Create two shapes on two separate shape layers. Select both shape layers and use Layer > Combine Shapes > Subtract Front Shape. It worked for me. Photoshop 26.2.0 on Windows.

This can definitely be a bit counter-intuitive.

Create your first elliptical shape.

With the layer still selected, and the handles still active (i.e. don't hit Escape)

Change the operation to Substract, and create the 'hole'.

I'd be inclined to drag out a pair of guides so you can get the 'hole' centred to the outer shape.