My approach (with LLMs especially) aligns more with what's outlined in "Growing OO Software Guided by Tests" (https://growing-object-oriented-software.com/toc.html). Chapter 4 there says "First, Test a Walking Skeleton", and Chapter 5 has "Start Each Feature with an Acceptance Test". I think it comes down to: get something working end-to-end first in a verifiable way, and then keep refining both the feature and its tests (preferable with TDD).

I've noticed that LLMs tend to generate multiple testcases in one shot (which is not how humans usually go about TDD), and also they don't start with Integration Tests, unless instructed to do so.