This thread is more about the Edition replacement experience, so I can appreciate the difference between this and the standard battery replacement threads.
I recently sent in a Ceramic Series 5 Edition watch, and while they bill you the full retail price of the watch (over $1500 in the case of the 44mm Ceramic), the replacement was very fast.
You can opt for the express replacement men service, as long as your battery meets their controversial 79% or less requirement, and they will send your replacement device first. Ironically, my watch also hung at 80%/81% for over a year, before finally dropping another few percent in a few months.
They did indeed send me a new-old-stock device. It comes in their generic packaging, but it is not a refurbished model as far as I can tell. When they receive my old device in as-discussed condition, the charge on my card dropped off.
I also have not set it up as I'm debating letting the next owner experience that, so I can't speak for the device's battery health percentage. Even new, a Series 5 watch is almost 5 years old.
I was pleased with the Edition service. Their requirement for 79% is indeed another story.