I can upgrade my ship and use my designs but I cant figure out how to make another ship entirely.
How to Build a Fleet in Story
Disable another ship by destroying it’s cockpit, then transfer crew to that ship.
You can now edit the ship as you see fit.
Or you can…
Alternatively, you can build a separate section for your main ship with a cockpit, reactor and crew, then separate that section entirely with an explosive charge, it will now function as a new ship.