This spell creates an Invisible, mindless, shapeless force
The "shapeless" part pretty much means the Unseen Servant force can not wear clothes the same way a human would. "Wearing" means letting the clothes take shape around the body.
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.
At least the mending and folding means, the servant can manipulate maybe two or even 3 things simultaneously, but more than that would quickly get out of both "simple task" and "a human servant can do" area.
Also, simple task pretty much rules out a task like "Serve food while making a cloak appear as if a human was wearing it". It'd be quite a stretch to call something like that simple.
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.
While it is not 100% clear if you can even abort a command, the "completes, then waits for next" implies it can not perform several simple tasks in parallel. If you give it a command to hold a cloak like a human, and then a command to serve food, it would drop the cloak (or possibly ignore the 2nd command as the 1st one is not completed).
A ruling based on above:
An unseen servant can hold one piece of complex clothing, such a hooded cloak, in a way that would resemble a human wearing them. Imagine something like a human servant crouching and holding up a cloak using their hands. So, especially from behind it could pass as a human - a decoy or a distraction, certainly.
It can just hold two or even three pieces, but then they'll just hang there. This would seem human only from far away or in poor visibility.
If there's a rack/mannequin for the clothes, an unseen servant can certainly carry that, if it's not too heavy, as suggested by another answer. But then you can't make the legs move etc, so... Hard to pass this as a human, too.
But then there's the problem: while performing this clothes holding task, unseen servant is unable to perform other tasks. That would not be simple task any more. So making it appear as a real servant doing servant things would not be possible without more magic. It's not clear from your question if this is what you need, or not.
Silent Image or Major Image might be more helpful than the Unseen servant holding clothes, though I see issues with synchronising the illusion to what the servant does....