Learn Hardcore Korean: hotel suyeongjange sugeoneul junbihae nohasseoyo. - Towels have been prepared at the hotel swimming pool.

에서 would emphasize the place where you performed the action (“I prepared them at the pool”), but then you lose the nuance of “they’re now sitting there waiting.”
에게 is for marking an indirect object (a person), so it doesn’t fit with locations.

What role does 수건을 play, and why use 을?

수건을 is the direct object of the verb 준비하다 (“to prepare”), so it gets the object particle 을. You’re preparing something (the towels), hence 을.

What does the grammar pattern -아/어 놓다 do in 준비해 놓았어요?

The structure (verb stem + -아/어) 놓다 means “to do an action and leave the result in that state.”

준비해 놓았어요 = “I prepared (and left) them,” implying the towels are ready and waiting now.

Why not just say 준비했어요?

You can say 준비했어요 (“I prepared them”), but it only reports the action.
Adding 놓았어요 stresses that it’s done in advance and the result still holds.

Is there a difference between 준비해 놓다 and 준비해 두다?

Both mean “prepare something ahead and leave it.”

놓다 focuses on “placing” the item.
두다 emphasizes “leaving” it in place.
In everyday speech they’re largely interchangeable.

Why is the verb in past tense (놓았어요) rather than present?

Korean uses -았어요/-었어요 for past polite. Here, the speaker reports that the towels have already been prepared.
If you said 놓아요, it sounds like you’re placing them right now rather than telling someone they’re already ready.

Could this sentence be expressed in passive form?

Yes. You can say 호텔 수영장에 수건이 준비되어 있어요, which means “Towels are (already) prepared at the hotel pool.” It focuses on the state (they’re prepared) rather than on who prepared them.

Can I rearrange the word order, for example 수건을 호텔 수영장에 준비해 놓았어요?

Yes. Korean word order is flexible because particles mark grammatical roles.

호텔 수영장에 수건을 준비해 놓았어요 is the most natural, but
수건을 호텔 수영장에 준비해 놓았어요 is also grammatically correct.