You do not go prone

Going prone (falling down so as to be flat on the ground) is the effect of gravity when going limp from being unconscious.

But there's no gravity in the Ethereal Plane

The Ethereal Plane also disobeys the laws of gravity; a creature there can move up and down as easily as walking.

So you don't fall down when you go unconscious. There is nothing to cause you to move, and the very concept of "down" is subjective in a place without gravity.

But do you get the prone condition anyway? Gaining the prone condition has three effects.

• A prone creature must stand up before moving (crawling excepted). This makes no sense here.

• A prone creature has disadvantage on Attack rolls. This is ostensibly because the creature's movements are restricted by the ground its lying on. This makes no sense here.

• Creatures have advantage or disadvantage on Attack rolls against a prone creature. This is ostensibly because a creature lying down takes less space and might have some form of cover. This makes no sense here.

None of the effects of going prone makes sense here. Without anything independently causing them to actually become prone (lying on the ground), a creature going unconscious in a place without gravity does not gain the prone condition.

You do not fall, go prone, or gain the prone condition

Going prone (falling down so as to be flat on the ground) is the effect of gravity when going limp from being unconscious.

But there's no gravity in the Ethereal Plane.

The Ethereal Plane also disobeys the laws of gravity; a creature there can move up and down as easily as walking.

There is nothing to cause a creature to move when it goes unconscious, and the very concept of "down" is subjective in a place without gravity. So a creature doesn't fall down when they go unconscious.

But does the creature gain the prone condition anyway? Gaining the prone condition has three effects.

• A prone creature must stand up before moving (crawling excepted). This makes no sense here.

• A prone creature has disadvantage on Attack rolls. This is ostensibly because the creature's movements are restricted by the ground its lying on. This makes no sense here.

• Creatures have advantage or disadvantage on Attack rolls against a prone creature. This is ostensibly because a creature lying down takes less space and might have some form of cover. This makes no sense here.

None of the effects of the prone condition make sense for a creature that isn't prone. Without anything independently causing the creature to actually become prone (lying on the ground), a creature going unconscious in a place without gravity does not gain the prone condition.