The other cases are the original request is still in flight or never occurred. The former case was explained by the prior comment, one request is processed, the other is returned by 409. The system cares little for which is which and neither should the caller. The latter case is handled by clients retrying until a request is received, at which point one of the other three states takes over.
Whether or not a prior request exists in the system in processed or unprocessed state should not matter in a properly implemented idempotent system, the whole point is that one and only one is processed, and all replicas indicate that they are such.
What you do inside of your boundary to implement that idempotent contract need not be part of the contract and the decision of what primitives to use (locking, content-based addressing etc) are mainly just a question of implementation constraints.
Whether or not a prior request exists in the system in processed or unprocessed state should not matter in a properly implemented idempotent system, the whole point is that one and only one is processed, and all replicas indicate that they are such.
What you do inside of your boundary to implement that idempotent contract need not be part of the contract and the decision of what primitives to use (locking, content-based addressing etc) are mainly just a question of implementation constraints.