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.