You have two options:
One, you can switch between showing the components you want to add, and the components on the ship
https://prnt.sc/t6ri55 It defaults to Race components, which is the parts you can add to a ship, switch to class components and you are shown and can remove parts from a ship class.
The other approach is to use wide view, that button is near the bottom right
https://prnt.sc/t6rj9w It will show class components, beside the race components list, so you can see both at the same time.