There's some more details on privacy at the bottom of the page:

> Audio Intelligence features are private by design

> a dedicated hardware-isolated compartment that processes audio in complete isolation from the rest of the system, then immediately deletes it

> Users are in control and [...] can decide exactly where and when Siri Recap takes notes, and can turn Siri Recap on or off at any time

> Siri Recap produces a brief, high-level summary of conversations — not a transcript — and is designed to exclude sensitive information like financial information or government-assigned identifiers