Eldritch Starship: Oh, there are a few.
Take esseli starships, for example. Unlike the link!n-Rechesh (who would be another fine example), they know better than to try to grow fully organic starships, so from outside the hulls and drives look relatively normal. Then you go through the airlock, and it’s all flesh, all the time, with heart-valve doors, neuron-cluster control interfaces, food-secreting glands, recycling intestines, and suspicious organic gurgles everywhere. Mining ships have refinery stomachs and tentacles.
Múrast starships are carved out of ice bodies, with the necessary technology fitted within, and then refrozen. Which is all very sensible when you consider their favored environment, but doesn’t explain why they always carve them into baroque cathedral-like structures rather than anything more utilitarian.
And then there are the seb!nt!at, who as creatures of nuclear forces that dwell deep within stars, do not build their starships out of matter in any conventional sense.
Starfish Aliens build Starfish Starships, basically, just as far as physics will allow.
The tortured structures built by rogue mining drones and other wild mechanicals are about as Gigeresque as it gets, though.
Tell me… these rouge mining drones wouldn’t happen to center around large, potato-shaped ships with wavy insect-style antennae on the front and twitching sets of spindly legs on the lower back, would they? 😀
Mainly they’re just colored red.
They’re also kinda… short.