While the PS5 version offers better ambient occlusion, LOD, anisotropic filtering, shadows, and some higher resolution textures, overall it's pretty clear that this game was designed with the last-gen consoles as a base. As such, it does feel that Modern Warfare II is being held back by last-gen.
This includes Cyberpunk 2077, Ghost of Tsushima Director's Cut, and Marvel's Spider-Man: Miles Morales, to name a few. Do PS4 games automatically upgrade to their PS5 versions? No, you first need to check if your PS4 game is eligible for a PS5 upgrade on this list from the PlayStation Store.