Historically it's varied by property (most I've had within a couple days, but I think some properties took 5-7 days to do it). I've had my one post-8/18 stay post within 48 hours. Maybe I'm old fashioned, but I almost always checkout at the desk and ask for a printed bill (or have them email it to me and I'll check on my phone to make sure I have it) before I leave, just in case something happens. Pre-merger, I only had to send in a missing stay request once, but it was helpful to have the physical copy!