That's a compelling three file format.
Have you considered a fourth file for Implemented such that Spec = Implemented + Design?
It would serve both as a check that nothing is missing from Design, and can also be an index for where to find things in the code, what architecture / patterns exist that should be reused where possible.
And what about coding standards / style guide? Where does that go?
That is interesting. So far we are just using the task list to keep track of the list of implemented tasks. In the long run I expect there will be an even more rigorous mapping between the actual requirements and the specific lines of code that implement the requirements. So there might be a fourth file one day!
Coding standards / style guide are both part of the "steering" files: https://kiro.dev/docs/steering/index