The plot thickens. After giving it 24 hours and with still no reservation showing on either UA or CO, I called UA customer service.
After a bit of browsing the agent first said "I see it on both sites, billed via CO" and then. "Ah, there is no FF number in the reservation." She added it and all is now well.
So, it looks like even though I was logged in and I carefully selected "Milepig" as the passenger, the system didn't record the number in the reservation. I wonder if this is an actual bug, or just a hiccup. Also puzzled about why the UA app billed me via CO (yes, I know they just cloned the CO app, but could they really have not redirected the billing to UA.) I just have a feeling that this trip will be trouble again before I'm through.