How big is the smart preview created by Lightroom

If you want a numerical answer, a 4K UHDTV computer display is 3840 × 2160 pixels, and a Lightroom Smart Preview is 2560 px on the long side, so if viewed at 1:1 magnification, a 3:2 aspect ratio Smart Preview will take up the amount of display area shown in the figure below. If you display the image at Fit magnification, the Smart Preview will fit the 4K screen, but of course it will not be using the full resolution of the display.

'Smart preview' is a misleading name. These are not previews at all. They are proxies for your originals, that's why their size is not depending on the screen of the device.

Smart Previews are always a maximum of 2560px on the long edge, irrespective of monitor type.