Etherealness lasts for 8 hours and doesn't require concentration:
You step into the border regions of the Ethereal Plane, in the area where it overlaps with your current plane. You remain in the Border Ethereal for the Duration or until you use your action to dismiss the spell…
A Short Rest is:
… a period of downtime, at least 1 hour long, during which a character does nothing more strenuous than eating, drinking, reading, and tending to wounds.
Meanwhile a Long Rest is:
…a period of extended downtime, at least 8 hours long, during which a character sleeps for at least 6 hours and performs no more than 2 hours of light activity, such as reading, talking, eating, or standing watch.
If I did nothing for an hour while on the Ethereal Plane, could that count as a short rest? Likewise, if I did nothing for the full 8 hours, would that count as a long rest?
Best Answer
Yes. Rest can be had on other planes of existence.
There is nothing inherent to the Ethereal plane that prevents rest.
It is not a safe haven
The Ethereal plane has dangers and monsters all its own. There is no guarantee that being on the Ethereal plane affords an hour, let alone eight, of respite.
Creature Encounters
Dungeon Master's Guide p. 49:
Ether Cyclones
These can be dangerous as they can transport those that get caught in them to the Astral Plane which has many dangers in addition to leaving the character stranded.