Hello, I am experiencing this on my iPhone 16 Pro as well. I don't know how this issue is not being posted more! you can barely find information on it.
I checked with 2 other friends who have an iPhone 16 Pro, the issue is present there however they did not notice it before I mentioned it to them.
Here is what I found out from my tests:
It does not happen for me on apple wallpapers, only personal wallpapers.
It does not happen if you enable "always on display" (you can remove the wallpaper to have a black background with the clock)
If you record the issue with slowmo its very obvious, the backlight of the screen is kicking in after the display is switched with a slight delay giving the laggy impression.
I don't want always on display or to use apple wallpapers... I really hope this gets addressed soon since I notice it every time I wake up the phone.