The basic rules include in the description of the Border Ethereal:
The DMG says (emphasis added):
A traveler on the Ethereal Plane is invisible and utterly silent to someone on the overlapped plane, and solid objects on the overlapped plane don’t hamper the movement of a creature in the Border Ethereal. The exceptions are certain magical effects (including anything made of magical force) and living beings.
Both forcecage and wall of force say that the effect extends into the Ethereal, blocking travel.
The unseen servant spell says:
This spell creates an invisible, mindless, shapeless, Medium force
The force cage and wall of force spell descriptions might lead us to conclude that only effects that say they extend into the Border Ethereal do, which is okay as far as it goes, except for that phrase in the DMG, "including anything made of magical force". That is pretty broad.
So, my question is:
Does an Unseen Servant on the Prime Material extend into the Border Ethereal?
Now, my initial reaction is to say that's ridiculous, of course it doesn't, and what kind of cheese is that, anyway? But then I thought, well, if not, why not? Is it because:
The unseen servant spell doesn't say it doesn't extend into the Border Ethereal? -- Okay, but what about that phrase in the basic rules? Is it just meaningless?
Or is it because the unseen servant is "a force", but not "made of force"? -- Maybe, but that seems like a distinction without a difference.
Is the phrase in the DMG just a mistake? -- Maybe, but they've had ample opportunity to clarify in Sage Advice, and haven't.
Or maybe the distance between right here and the Border Ethereal is "more than 60 feet". -- I think the distance between here and the corresponding spot on the Ethereal is infinitely small, not infinitely large, but that's debatable, so maybe?
Or is it because if unseen servants extend into the Ethereal then complete shenanigans ensue? -- Maybe there's a point to this argument, I can't find one better.
Or some other reason?
So, finally, given that phrase in the DMG, "including anything made of magical force", if an unseen servant doesn't extend into the Border Ethereal, why not?
This isn't just theoretical. If I have an argument to stand on I'm going to discuss it with the GM. The "Maximally Cooperative GM" might allow it, but mine's probably just going to give me that look and say, "hard no", but it's worth a shot. I'm sure an unseen servant extending into the BE has to be good for something.
For instance, maybe it can be used to transfer or hide items in the Ethereal. Perhaps using see invisibility I've spotted something interesting, a chest perhaps, and the unseen servant could open it.
Or maybe it's a distinction without a difference, and there aren't any shenanigans. Living beings in some sense extend into the BE, and it doesn't seem to matter.