I personally think that there is absolutely nothing inherently bad with using AI for code as long as the result is not trash, which unfortunately AI still does generate quite often. So I frequently use AI to generate a 'proof of concept', but I take it as a rule to never ever copy-paste code from AI directly, instead using it as a reference to write code myself. Not because of some prejudice, but because due to the nature of LLM models, AI is exceptionally adept at generating 'almost correct' code, with subtle errors which make is very difficult to debug, especially if you did not take time to understand it. FWIW, I do the same with all the code I get online, even from comparatively reliable sources like Stackoverflow.

Same thing goes for learning -- advanced AI models act very good in teacher role, with infinite patience and boundless erudition. However, they can easily and convincingly mislead you, simply because of random fluctuation of one of hundred billion neuron weights. So when I use AI to learn something, chat with it to get a quick understanding, and then go look at original source (in your example it would be A* paper or some textbook on algorithms) to make sure there is no mistakes in my understanding.

I believe in a few more years of progress those concerns will diminish, but we are certainly not there yet.

The line between AI assisted and AI generated. For such a line those two would have to be on the same scale and increasing something would make it switch over from one state to the other.

For walking and running that is speed and the line is when both feet leave the ground.

What is the something that changes for AI involvement? I guess it is decision making and sample size. But it depends on the context. If a photographer takes 1000 pictures and selects 1, did he create the photo? Or was it the camera and the objects that were photographed? Does an orchestra conductor create music?

Those two are generally considered art. But if you prompt a gen AI system to make 1000 pictures after your direction and select 1, it currently is not considered art, and it is debated if it counts as creation. And the selected image will be AI generated, even if you change something, because an image is a big sample size.

For code creation you have templates and text book examples, discussion threads and existing code to copy from. Was it you, that made the code, if you copied it and modified it? If your sample size or your own deciscion making for the modification are  sufficient to not violate copyright, yeah, you made it.

So, for code generation, I would put that line at the point where you let the AI do basically the game mechanics, instead of parts, like algorithms and functions. Also, you do not ask AI to give you 1000 functions and chose one. If it works, it works, if it does not, you make it work. 

And for image generation, that line is shifted. If you ask an AI to draw the hands on your stick figure or you have the AI make the stick figure and correct the hands, both those big samples are AI generated. 

As for the rules on Itch, if you do not have AI artworks and merely AI "assisted" code, but not large portions of AI code, I would just leave the disclosure blank for the time being, if possible. That disclosure feature has a lot of issues, both in the declaration and how the feature is useable for players. I have yet to see someone lamenting about how bad AI code games are, which makes me think, that players do not care about the code. They care about story and art works. But Itch lumps all "AI" together with their "no-ai" filter. 

For normal minded people (applicable to art and to programming):
-AI assisted: you used AI to generate something, then worked on it, or used it as reference, or mixed generative and manual work in some amount, or you made things like the concept, styles, and pose, etc of the final generated image, so it involves a decent amount of conscious work and not a purely random one. Then you may even paint over it, or change it manually, or repeat this whole process lots of times until you get the final thing.
-AI generated: you just select one or two things, and pushed a button, then you got a random image.

For against-generative art fanatics: all is AI generated and crap.
For pure AI-fanatics: this kind of people almost doesn't exist, so usually doesn't happen, but I met people who disliked everything that was not purely generated and didn't want to even postwork an image.

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.