as you have stated 'And yes, this project was built almost entirely with Claude Code with a bunch of manual verification and testing.' this code is not copyright protected, therefore you are not allowed to apply a MIT LICENSE to this project.
That has not been established in the courts, at least not precisely enough to assert that for sure this project isn’t copyrightable.
“ But the decision does raise the question of how much human input is necessary to qualify the user of an AI system as the “author” of a generated work. While that question was not before the court, the court’s dicta suggests that some amount of human input into a generative AI tool could render the relevant human an author of the resulting output.”
“Thaler did not address how much human authorship is necessary to make a work generated using AI tools copyrightable. The impact of this unaddressed issue is worth underscoring.”
