If your iPhone 16 Pro screen is delayed when waking up after the iOS update, it may be due to a software-related glitch affecting display responsiveness.
This issue has been observed particularly when custom wallpapers are used or when the Always-On Display feature is turned off.
To reduce the delay, try enabling Always-On Display in Settings > Display & Brightness and consider switching to one of Apple’s default wallpapers, as these seem to be better optimized.
You can also check under Settings > Accessibility > Display & Text Size to see if toggling options like Reduce Motion helps improve responsiveness.
If the issue continues, it’s likely a software bug that may require a future iOS update from Apple to fully resolve, so consider reporting it through the Feedback app or contacting Apple Support.