Trying to throw window to different desktop doesn't work

I have a shortcut to work with yabai to "throw" a window to a different virtual desktop, its shift + alt + # where the # is the number of the desktop i want to throw it to. however, this just makes it not part of the windows tiled and it stays on the same desktop, then when I go back to the desktop it was on it becomes part of the tiled windows again.

Start by reproducing the Shift+Alt+# shortcut while yabai manages tiled windows and virtual desktops, then investigate the interaction between skhd and yabai. Done means the focused window is moved to the selected desktop and remains correctly included in tiling when returning to the original desktop.

Written by the indexing model from the issue text.