I'm also in a very similar situation. I suspect your assumption here is correct:
"My assumption is the iOS app is using an embedded Safari browser that for some reason can't play with Conditional Access"
I can see the sign request coming form:
Browser: Mobile Safari 16.2
Operating System: iOS 16
however, no Device ID is displayed.
Going deeper into troubleshooting:
The device is clearly joined and compliant, it was confirmed in Intune and by looking up the device info.
Now I wonder what's stopping Safari to pass the Device ID onto the auth flow?
**For those stumbling upon this discussion:
The issue of the in-app browser (Safari) not communicating Device ID with CA was resolved by deploying the following configuration profile:**
[https://learn.microsoft.com/en-us/mem/intune/configuration/use-enterprise-sso-plug-in-ios-ipados-macos
Enterprise SSO plugin resolved our issue and I successfully authenticated with a compliant iPad based on device ID/compliance.