I’ve always struggled with what should be in Claude.md that doesn’t belong in readme.md or a similar supporting file.
I tend to include a well documented justfile, so between the readme and that common commands are covered. If there’s a style guide it should be its own file, or summarized in the readme.
If Claude is making errors I tend to just update my global Claude file, but I haven’t updated it in 6 months — only to disable Claude signatures on generated commit messages.