Earlier quoted context omitted.
Retries will only receive 409 if the original request was successful. If the original request failed, the server performs the operation as normal on the second request. It doesn't replay failures. The whole point of the idempotence mechanism is so you can make a reliable distributed system. If the first try fails, the client doesn't know if it succeeded or not, so the client should try again later ("at-least-once").…
What if the original request is still being processed when the retry comes in? That doesn't fall into either of your categories: the request isn't successful, but it hasn't failed either.
If it processed 99% of the request and the final bookkeeping failed because of a duplicate, that's still a failed request.
Arguably this should be the primary way you check for idempotent requests - you shouldn't have a separate check for existence, you should have the insert/update fail atomically.
This is the same thing you see on filesystems for TOCTOU security holes - the right way is to atomically access and modify once, and you only know the request was already processed because that fails.