I have searched for a solution to this problem and I have found many answers, all of which tell me that this is not an issue with Photoshop, but an issue with Windows. They will tell me: "The Windows clipboard does not preserve transparency of a PNG image".
The only problem is, when I paste such an image into the free, open-sourced image editing program Paint.Net, there are no issues at all and the transparency is retained just fine. This would imply to me that the Windows clipboard is preserving the transparency, and Photoshop is somehow turning it black.
Does anyone know if there are some settings in PS keeping me from pasting transparent PNG images?