Relevant parts of Unseen Servant spell:
This spell creates an invisible, mindless, shapeless, Medium force that performs simple tasks at your command until the spell ends. The servant springs into existence in an unoccupied space on the ground within range.
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you can mentally command the servant to move up to 15 feet and interact with an object. The servant can perform simple tasks that a human servant could do, such as fetching things, cleaning, mending, folding clothes, lighting fires, serving food, and pouring wine. Once you give the command, the servant performs the task to the best of its ability until it completes the task, then waits for your next command.
It clearly takes the space ofseems to have size comparable to a Medium creature, and it has position. It seems to me that RAW, it can not take hide action (or any action in the rules sense), so it would never be hidden. There is no DC for detecting it given, which supports this interpretation. However, this RAW interpretation does not really make sense, because it is invisible and does not in itself make any noise, so it sounds like it is undetectable unless it interacts with an object, even if it is not hidden.
So, how to rule on detection of existence and location of an Unseen Servant?
Let's narrow this down by saying that no Detect Magic, Truesight or other such spells or abilities are in use. Also let's leave blindsight out of the scope.
There are several cases, starting from it simply idling and waiting for command: is it possible to know it is there and has not moved, and how to describe this situation to the players? Is it possible to even detect it moving in unobstructed space, if it's not carrying something? What about when it performs a task such as pouring wine, is it possible to distinguish an Unseen Servant from an invisible Mage Hand when all you actually see is just a bottle moving by itself?
It seems this is one of the many things the DM just needs to make their own ruling on, but what do the rules say about this, did I miss something?