I've done some more testing, and here's what I've learned.

The Kasa app creates a sub-directory; Android Device Name > Internal Storage > Pictures > Kasa , in which it stores copies of the selected icon image (regardless of the icon's original source... albums, camera, doesn't matter). The copied image will have the filename "kasa_crop_<40char hex string>.jpg". also created will be a second copy, with filename kasa_background etc. etc.

It is the image copies that Kasa is creating that is somehow going wrong; each generated copy is literally 5 pixels by 5 pixels in dimensions, and 401 bytes large, suggesting the app's image compression/resizing code might be at fault. Perhaps the calculation has a decimal error (intending to create a resized image of 500x500 pixels maybe?)

Once Kasa has created all these squished files, there is a workaround. You can copy the exact filename that is generated, then replace the Kasa-created image icon with your original intended image, albeit renamed to use the Kasa-generated filename. This then appears in Kasa as you would expect it to