> In sway I'd pop open the new window, then drag it to the top or bottom half of the window I want it to share horizontal space with

I did not even know it was possible to drag windows. I do that by selecting the window I want to split, then setting a "vertical" split with "Command + v", then creating the new window (usually a terminal).

Or I move the window with "Command + Shift + [hjkl]".