I figured out how to copy and paste in build mode. Just select a block (or multiple) and use ctrl+c to copy them and ctrl+v to paste them. They'll be placed in the same position as the original block, so you'll need to drag them away with either the arrow or the cursor icon. Hopefully this helps someone later. The pasted blocks will inherit all properties of the original selection.

For anyone who hasn't found build mode yet, click the + icon from the three icons in the top middle of the play menu next to the search bar.

.....ctrl C and ctrl V wasn't your immediate assumption on how to paste blocks?