No it does not count as hand built. In the same way that a human pressing buttons, such that an automated production line makes a watch, and then at the end a human goes and looks at it and says "yup that's a watch" isn't a hand-made watch.

You're not making all the decisions in that case. You're making approvals and steering but the agent is making decisions and is framing what is even available to you to approve. When you build something by hand, you make decisions as you go in a way that the agent is now replacing.

Directly equivalent to having outsourced it to a shop of remote consultants where you remained as onshore lead. And in all those past cases we would have said "No."

In the age of LLMs we can assume that any code was generated by an LLM unless noted otherwise, so I think it is fair to not point out the use of LLMs. However, words like hand built should be reserved for the instances where the code was actually written unassisted. Reading all the code means nothing, there is no such thing as code that was written as if you had written it, unless you have written it.