iPhone XR not seeing iOS 13.1 update
The sure fire way to get an update now is to use Apple Configurator 2


https://support.apple.com/apple-configurator
Connect over USB and update


OTA updates are staged and depend on caching / CDN and other things out of your control the first 7+ days of a major release in my experience. One way you could pick this apart is to use USB networking and capture the traffic between iOS and Apple’s update servers and perhaps see an error condition.


https://developer.apple.com/documentation/network/recording_a_packet_trace


Charles Proxy is excellent for this sort of deep dive as well when networking isn’t working.

The above tools do not need Apple support or a paid developer account. The below option I believe is only available if you have a log in as a developer or Apple sends you the profile as part of a support engagement.

There is a software update debug log profile and if you instal one that’s properly signed by Apple, you can get text logs from your specific device to answer why it’s not updating or perhaps know when the checks happen or what might be blocking them:


https://developer.apple.com/bug-reporting/profiles-and-logs/?platform=ios&amp;name=Update


The above documentation has a PDF guide and the Configuration Profile required to enable logging for this situation.