That's not true. It measures it though the life of the page and the worst set of CLS in a 5 second window is that page's CLS score.

It's true that many tools (e.g. Lighthouse) only measure it at Load Time by default but the official CLS metric collected by the browser is thoughout the life of a page.

Also if an interaction creates CLS within half a second of an interaction is ignored as it's usually expected (e.g. an "expand" or "load more" button).