For the purpose of seeing the effect of sharpening, I would like to be able to put the same image on the screen twice.
I would then zoom into both equally, but only sharpen one - comparing the changes in the sharpened image with the other one.
Can I do this?
Yes, just create 2 variants of the same Raw file, select a file and clone it so it will be exactly identical with all the settings. Then select both (click in the Browser with the CTRL or Command key pressed), deselect the "Edit all selected variants"
selector (see attachment where it is still selected), and toggle the "Multiview" viewer mode on. Now select one of the identical images and apply sharpening to that primary variant, without affecting the other variant.
When you zoom in, hold the Shift key to zoom both in simultaneously. I use the scroll-wheel of my mouse for zooming because it then zooms in/out to the mouse pointer position.
When you are done, toss one of the variants or keep them both for future adjustments.
P.S. I saw that you already figured it out as I was posting my answer.