On the Mac it works to start dragging a file from one place and, while keeping the dragged file selected with the mouse/trackpad, using Command-Tab to switch to another application. If that’s the Finder, once there Spring-loaded Folders can be activated/navigated while retaining the selected file.
One must-have app I put on any macOS install is Yoink, which gives you a "shelf" you can drag anything onto, then drag out later when convenient. Handy when the target app you're dragging to hasn't been opened yet.