Is there a method to target an open Finder window from the "Save" dialog?
The specific software you are probably alluding to is Default Folder X - which even allows you to click through any intervening windows to return to a folder visibly open on the Finder desktop. It also has a pre-determined list of 'useful' places &amp; a history list. I do consider it one of the indispensible utilities on Mac.

Alternatively, macOS itself allows you to drag any visible folder onto a file-picker dialog to send the dialog to that location.

Fullscreen apps may interrupt either of those efforts - but I have a particular set of reasons I absolutely never use fullscreen, so I'm not certain how it will respond.