Thank you so much for helping！ Could you help me with one more similar question: What's the difference between:'I need to buy a new pair of running shoes, so I'm going to the sports shop.' and 'I need to buy a new pair of running shoes, so I'm going to the sports shop.' Thanks a lot!❤️

If it's a new kind, then it's new. If it's new, then it's a new kind. "Six and half dozen of the other", as they say. Both are puzzling though. We speak often of new dishes, new recipes, and new menus, but new "foods" are something only a chemist would dream about (and I wouldn't want to eat any of it).

The second sentence doesn’t make sense because ‘new food’ isn’t a category with any meaning. The first sentence sounds ok but I doubt that it is correct either. That is because there are already many kinds of food and it’s unlikely that a new food won’t fit into an existing category, though I guess it could theoretically be the case. She’s got an idea for a new food. She’s got an idea for a new (candy, breakfast cereal, etc)

The first one sounds better, you could substitute the word "type" for "kind". The second sounds better with the word "type", a type of new food. They are really the same but the second sentence is poorly phrased.