I am trying to describe the act of an official attaching a medal to a recipient's clothing (chest) during an awards ceremony. Is "to drape a medal" the correct usage? I don't think "to pin a medal" sounds formal.
I don't believe to pin and to drape differ at all in terms of register or formality. The difference is semantic:
pin (v): attach or fasten with a pin or pins in a specified position.
drape (v): arrange (cloth or clothing) loosely or casually on or around something.
You may find examples of "drape a medal around someone's neck," but the action you want to describe - "attaching a medal to a recipient's clothing (chest) during an awards ceremony" - is clearly one of pinning, not draping.
As a side note, we do have the following expression in English, which is a caustic way of responding to someone's boasting:
Would you like a medal or a chest to pin it on?
This is just me talking from 30 years as a florist... (seen a lot of funerals) The only time I've heard "drape" a medal, is when someone puts it on a dead body lying in state, or on the casket. (Or, on a likeness of the recipient.) I don't think you use "pin" or "award" in the case of actually presenting it posthumously.