I know roll-outs are staggered, but 10 days (and two minor releases) later I'm fairly sure I should have been offered an update (all other iOS/iPadOS devices in the house have been).
I've restarted the phone, logged on to various networks (plus cellular), and I'm still seeing
iOS 13.0
Your software is up to date.
When visiting Settings / General / Software Update
Automatic updates are On, iCloud setup is fine (backups working, etc.), and this phone is not enrolled in any betas. The update from 12.x to 13.0 was via iTunes, but I've done that before and (as expected) it's had no effect on future OTA updates.
Any magical bonus steps I might take to cause the phone to discover the update?