If you want to have an LLM write your README (and other docs), I've found it useful to add a DOCS-GUIDE.md to your project and write your conventions and expectations there.

Google has a two-part technical writing crash course:

  - https://developers.google.com/tech-writing/one
  - https://developers.google.com/tech-writing/two

I've had good success with adding a directive to the guide that points to those two URLs and tells the agent to adhere to them in all of its documentation.