I recently built a keyboard (previously I had only added switches and keycaps), and in the box, I see some standoffs. From what I can tell, these are optional? It seems some people use them and others do not depending on their plate material. Is this true, or are they absolutely needed?
It depends on case material and mounting type. But generally standoffs create separation and stability between the PCB and case, especially with tray mount boards.
Some people reduce the number of standoffs in certain areas to allow more flexibility in the PCB. But, if your keyboard case material is metal, and you have no standoffs, or the PCB is flexible enough to contact the case, it can short the connections which may cause switches to malfunction or behave erratically.