So first of all, that analogy with the wood toy is a bit vague. The metal part might have been made with a CNC machine or die cast - or it could have been made on a manually controlled lathe. In the second case, most people would call it "handmade", the same way that handmade clothes may have been sewn using a machine.
If the metal parts were made with automated tools, then I would absolutely say that the tool is partially made using automated tools, and the phrase "handmade" would require some very major asterisks.
I also do not think these distinctions matter when it comes to the Internet Plagiarism Machine. Personally, I do not care if 5%, 50% or 95% of a product were made by a virtual dumbass that makes slop by stealing from other people en masse. It is tainted for me in all of these cases. The only acceptable percentage for me is zero.
I am far more lenient when it comes to "handmade" artisanal products - like, i would not complain about a "handmade" chair using off-the-shelf screws, but those screws are not a good analogy for AI-generated boilerplate code because the machine that makes the screw comes with far, FAR fewer ethical issues than the Internet Plagiarism Machine.
So personally, I think the binary "yes/no" question is absolutely fine. Even making the distinction between AI-made graphics, text, code and audio is a step too far, in my opinion, because to me it implies that using the Internet Plagiarism Machine for "art" is fundamentally different than using it for code. It isn't. Both of these uses just output slop based off the stolen works of others.