I'm stuck here too, I assign all of my crew to their duties but it won't let me travel, it keeps saying "you need to assign all your duties" but I have no one left to assign.
Just to be clear, duty assignments are different than assigning crew to their bridge stations. If you are having issues with the duty assignments, feel free to swing by the discord if you get a chance and send me your save file, as I can't reproduce the issue here.