See FUIAction CopyAction and FUIAction PasteAction in SDetailSingleItemRow and SDetailCategoryTableRow.
For example we will look for SDetailSingleItemRow.
The actions runs either SDetailSingleItemRow::OnCopyProperty or SDetailSingleItemRow::OnPasteProperty.
Those use FPropertyEditorClipboard functions such as FPropertyEditorClipboard::ClipboardCopy and FPropertyEditorClipboard::ClipboardPaste.