Action for moving window from arbitrary space to current space

Hi, I'm looking for a way to move a window from another space to the current space without having to switch spaces. This is relevant for me to e.g. move a chat window that I've already opened in another space to the current space. In the mission control settings, I have When switching to an application, switch to a Space with open windows for the application disabled and want to keep it this way for various reasons. (So when I cmd + tab to an application with no windows in the current space, I don't automatically move to a space with open windows for this application.)

The detailed workflow from a user's perspective would be:

  • use cmd + tab to switch to the chat application (chat window is not shown as a result of this because it's located on another space)
  • use a BTT keyboard shortcut to move the chat application window (that is already open in another space) to the current space
  • chat application window appears in current space

I've already found the "Custom Move / Resize Window" action but it seems to not quite do what I want and also seems to have no other effect.

It would be nice if this workflow would not require the window's title (unlike "Custom Move / Resize Window") but could be universally used targeting the open window(s) of the currently selected app (currently selected app = app whose name appears in the top menu bar).