I don't think what you are doing would count as "generated content." What you are doing is similar to copying a few code snippets from tutorials.
Now if you were having an LLM spit out artwork, audio, levels, and other assets that you simply plop into your game, then you would need the tag.
From https://itch.io/docs/creators/quality-guidelines#accurately-tag-your-use-of-gene...:
Generative AI refers to artificial intelligence systems that create new content (text, images, music) by learning from large datasets. This includes large language models like ChatGPT and image generation models like DALL-E, Midjourney, and Stable Diffusion that create new outputs based on training data.
We ask that you accurately tag your project if it contains materials produced by generative AI by utilizing the AI Disclosure section on your project’s edit page.
They don't even mention code here, and it's not like you are generating pages of code anyway, so I think you should NOT use the tag.