96 DPI when creating a new file from clipboard was a surprise to me, too. It is intended behavior in Affinity apps on Windows.
To avoid 96 DPI, I created a 72 DPI document preset that’s the size of my screenshots — in my case it’s the size of 2 monitors. Instead of pasting from clipboard, I create a new document from the preset and paste into that. But, not much help if the copy is from a selection.