There is no way to display two computers on a single monitor.
However if both computer are hooked to the same wifi network, you should be able to make a remote connection from the new computer to the old one. That will allow you to open the contain of the old computer in a File Explorer window on the new computer. You will be able to see all the files and folders and then copy from that window to the new computer.
Open a File Explorer window. In the bar at the top type in
The old computer’s C: will open in the window.
Then you copy whatever you want form just like you would copy files between any two folders on your computer.