Don't treat the Unseen Servant like a creature
As was noted in this answer to this question, the Unseen Servant is not a creature. What it does and how it acts is pure magic. The granular detail you are asking for is left for a DM's ruling.
What Was it Like in Previous Editions?
Since you asked for lore and previous editions, let's look at:
AD&D 1e (TSR, 1978, PHB p. 69). It was a first level Conjuration
spell as it is now.
The unseen servant is a non-visible valet, a butler to step and fetch, open doors and hold chairs as well as to clean and mend. The
spell creates a force which is not strong, but which obeys the
command of the magic-user. It can carry only light weight items, a
maximum of 200 gold pieces weight suspended, twice that amount moving
across a relatively friction-free surface such as a smooth stone or
wood floor. The unseen servant cannot fight nor can it be killed,
as it is a force rather than a creature. It can only open normal doors, drawers, lids, etc. It can be magically dispelled, or
eliminated after taking 6 hit points of magical damage.
From the SRD for D&D 3.5 edition, the description is very close to
the 5e description, using the words "invisible, mindless, shapeless
force." It is Conjuration magic, cannot attack (has 6 HP), has an
effective strength score of 2, and has a speed of 15'.
It cannot be killed, but it dissipates if it takes those 6 points of damage from area attacks. It gets no saves against attacks.
It appears that "it's not a creature" has remained as a governing
principle. Unlike a creature, the 3.5e Unseen Servant does not have
What are its limitations?
Could an Unseen Servant (a magical force) move through the air (while staying within 60' of the spell caster?) As the rules do not specify, the DM can rule either way. For a mundane example, have the US close the shutters on a window that is out of reach.
Could the Unseen Servant reach/move up to that window 15' feet off the ground to close the shutters? That's a household function within the bounds of the spell and less complicated than mending clothes. I'd rule that it could, but another DM might not. A valid ruling would be that the US needs to get that pole in the corner and use it to reach up and close the shutters. A regular servant would do likewise.
This spell creates an invisible, mindless, shapeless force that performs simple tasks at your command until the spell ends.