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?