If it contributed significantly to the design and execution, and was a major contributing factor yes. Would you say a reserve parachute saved your life or would you say you saved your own life? What about the maker of the parachute?
I'd be thanking the reserve and the people who made it, and credit myself with the small action of slightly moving my hand as much as its worth.
Also, text editors would be a better analogy if the commit message referenced whether it was created in the web ui, tui, or desktop app.
I suppose that for me the tool rarely contributes to the design and execution. At work and for any project I care about, I prompt once I know what I want, in terms of both function and the shape of the program to do it. If the model gen matches the shape closely enough, I accept, otherwise iterate from there. To me this is authorship.
When I vibe code - which for me, means using very high level prompts and largely not reading the output - then I could see attributing authorship to a model; but then I wonder what the purpose of authorship attribution is to begin with. Is it to tell you who to talk to about the code? Is it personal attestation to quality, or to responsibility? Is it credit? Some combination of these certainly, but AI can hold none except the last, and the last is, to me, rather pointless. Objects don't have feelings and therefore are unaffected by whether credit is given or not; that's purely a human concern.
I suppose the dividing line is fuzzy and perhaps best judged on the basis of the obscenity rule, that is, I know it when I see it.