Claude Code has output styles; one of the predefined styles is Concise [1].

    Concise: Claude leads with the result, skips preamble and narration, and
    keeps responses short by default, while doing the engineering work as
    thoroughly as in the Default style. When you ask for an explanation or
    more detail, Claude answers in full. Claude always keeps the complete
    content of error reports, security warnings, and confirmations for
    destructive actions. Requires Claude Code v2.1.237 or later.

Output styles are just more context (like CLAUDE.md) with a tiny bit more weight. They very much don't force Claude to speak succinctly, no matter what you put in them.