Some other topics with a similar issue, with the last one being from NEXT.
Make sure you have progressed enough with the Overseer and Scientist to be able to build the Weapons Terminal. Make sure to build this terminal inside a prefab construction like a powered Cuboid/Square/Round Room. Not always does it get correctly recognised inside a different custom structure.
If the Vykeen to hire can not be found in the current system’s space station, ignore the mission icon and try to visit neighbouring Vykeen systems and talk to every Vykeen in the space stations. Not always is the person to hire found inside the separated room.
Building the Exocraft Terminal will likely not work, as this is a mission that comes later with its own requirements. Bypassing steps required may mess it up even more.
This mission has been buggy ever since NEXT, make sure to report it to https://hellogames.zendesk.com/
Note:
If all fails, try warp to systems away from the base, until the option to reset the mission in the Quest Log becomes available; middle mouse button on PC