How to stop Finder window from disappearing during drag and drop from Chrome?
Your Chrome Downloads history is here

chrome://downloads/

the actual download is already on your mac in the specified folder.

To specify where to download from Chrome, go to settings > Downloads.

The bar at the bottom of the Chrome window is FYI only, not the place where the downloads reside.

The downloads are already on you Mac and you do not have to drag them to the Finder.