When moving window from one screen to another, the swapped window is then focused

[ibrokemypie]

If you have a window on monitor one, and another window on monitor two, then move the window from monitor one to monitor two, the window that was on monitor two and has been swapped to one takes the focus, rather than focus staying on the window you were moving.

[ntrrgc]

then move the window from monitor one to monitor two

the window that was on monitor two and has been swapped to one

No window has been swapped from monitor two to monitor one in your explanation, it was the other way around.

Please provide a clearer step sequence to reproduce the issue, including the right-window commands you ran. Also please specify your desktop environment and which variant of right-window your are using (X11 or bspwm).

right-window is stateless, so moving windows should not alter its behavior compared to having them being there on the first invocation.