Actually, it is entirely possible your new phone does have a genuine Apple screen. Starting with the 3rd gen iPhone SE / iPhone 12, Apple started pairing the display to the motherboard. Up until iOS 18, only Apple could pair a new screen to the logic board unless you used the self repair program. So for anyone else who wants to replace their own screen, you got used to the idea that you'd get a genuine screen warning whether or not it was a genuine Apple screen.
On some models there can be a loss of auto brightness and you would have to use a device programmer to reenable True Tone, which appears to have been done, so it looks like your only issue here is the genuine parts warning.
I'm not up to date on the new repair capabilities of iOS 18, but there's a chance you may be able to get rid of that warning using the new Repair Assistant feature, assuming it is a genuine screen. You can find more information about it on Apple's site.
[link|http://support.apple.com/en-us/120579|Use Repair Assistant to finish an iPhone or iPad repair - Apple Support]