[topaz0]

You can absolutely do this in i3 or sway. There aren't default keybindings for doing it, but it is easy to set up your own. I set $mod+equals to 'move workspace to output up' in i3 (or something like that -- I'm not on that machine to check). This works for me since I set up my external display to be above the laptop screen, so it effectively means 'move this workspace to the other output'. You could also specify a specific output to move to, or change what the direction is.

[icambron]

That's not quite what's being asked for. I think it's more like super+1 for "move workspace 1 to the current monitor". I haven't quite figured out how to do that in sway, although I'm pretty new with it.

[topaz0]

In my scheme that move is just two key combos away, which seems fine to me, especially since it is rarely what I want. You could make it one key combo if you want, too, in a script if not in a single line.