Hello Andrei. As a kitchen appliance enthusiast, I can thoroughly explain why this discrepancy exists between the manual and online advice.
When manufacturers state that preheating is necessary, they design their cooking time charts around a hot basket to ensure food begins searing immediately, which prevents moisture loss and gives a better crisp. However, many home cooks find that skipping it works fine for foods with high fat content or longer cooking times, as the air fryer heats up almost instantly anyway.
If you want to ensure optimal texture for your meal prep, especially for smaller items or things that benefit from a quick crust, following the manual's preheat step is recommended. For convenience on busy weeknights, skipping it usually turns out fine, though you may need to add a couple of minutes to the total cooking time.