How can I send a window to a different workspace without changing the active workspace?

I am not using Gnome right now, but I see under Focus or open window in gnome on keyboard shortcut that wmctrl works with Gnome.

So, I paste from an answer under the question you linked (on Xfce):

Move active window to workspace 1:

wmctrl -r :ACTIVE: -t 0  

Move active window to workspace 2:

wmctrl -r :ACTIVE: -t 1 

Move active window to workspace 3:

wmctrl -r :ACTIVE: -t 2  

Etc...

No such shortcut is listed for standard GNOME3.

Your virtualdesktopopenhancer is dependent on the Windows-only AutoHotKey to implement the MoveWindowToDesktop feature you describe.

However, there are similar Open Source apps for Ubuntu and Linux, Autokey may help, if you take virtualdesktopopenhancer apart and find the bits which do what you need. The AutoKey Forum may be of assistance.

Sadly, IronAHK, designed to be a rewrite of AutoHotKey, is discontinued. Maybe it works for you, maybe it doesn't, but support for IronAHK is unlikely.

Easier answer...

Use GNOME Tweaks to enable the "Activities Overview Hot Corner". This will allow you to move the mouse pointer to the upper-left corner to expose the docks and workspaces.

Use GNOME Tweaks and enable "Static Workspaces". I have mine set to four.

Identify the window you wish to move. Expose the docks and workspaces. Drag the desired window to another workspace in the workspaces dock. Click on any open window in the current workspace, or any open window in an exposed workspace, to close the exposed docks and workspaces. (and/or, click on any exposed window/workspace to also change to it.)

In 19.10, existing Keyboard Shortcuts exist to move windows to specific workspaces.