Can you tell us if the "burn" goes away after a while or if it shows at the same intensity always? In my case, when I use dark mode, I can see an image retention (very common in OLED screens) of the cellular, Wi-fi, battery icons, and the home bar that goes away after a couple of minutes if those areas are showing another image. When I use the clear mode, this problem usually goes away (since those pixels are showing black most of the time). On the rest of the screen, I can't see anything in particular.
If this is a software problem, my theory is that the iOS code for iPhone 15 (not the pro models) probably doesn't have the fix for the display image retention that happened to the pros a couple of months ago. If this is the case, I hope they can fix it soon with an iOS update.
If the burn that you referred to is not going away, maybe it might not be image retention, but something worse. Do you know if you left your phone showing the home screen for a long period at max brightness? Regardless of the reason, Apple should replace your phone or your screen without questioning, since OLED burns on iPhones are rare, and since your phone is still covered by the warranty. Maybe you could try another Apple store.
Anyway, I will also schedule an appointment at Apple to see if this problem is normal behavior or not, and I will update you about it :)