Now that we've seen their prevos, their typing and abilities make a lot more sense. They're not actually organic lion/bat creatures, they're the tiny little head seen inside the midstage cocoon.

So Solgaleo is actually a little head piloting a mech suit/armor containing cosmic energy, hence Psychic/Steel and Full Metal Body. Meanwhile Lunala is a head with skeletal hands protected by a web of cosmic energy (Shadow Shield) and most of its "body" is noncorporeal, hence Psychic/Ghost.