This has happened to me three times that I can recall. Twice I got my items back. The third time, which happened to be two nice shirts, I'm sorry to say, they never turned up.
What the manager
should have done: "I'm sorry, sir, it does not appear that anything has been turned in thus far. I will speak with the guests that now occupy the room and find out if they found your shirts when they checked in, or if perhaps they are are there and they haven't noticed them. What number can I reach you at once I'm able to speak with them?"
Then, she should have personally gone to speak with the "cleaning technician" and her "styling manager" (

) about the situation.
Next, she should have called the room. If no answer, left a message for the new occupant to call her and slid a note to the same effect under the door of the room.
You can't tell me that, if handled appropriately, the new guest in the room is going to be offended at being asked that question by the hotel manager. In fact, it could even make the person feel confident that if he/she were to ever leave anything behind, the management would do what they could to help locate it.
This kind of thing doesn't have to be so hard.