In the section Design > Full-Page Overlay would be good to consider the option to disable scrolling in the content of the page while the banner is displayed. We are now solving it via CSS, but it should be fine to solve it via javascript on the Cookie Script side.
Our CSS (which is slow in the browser)
body:has(div#cookiescript_injected_fsd) {
overflow: hidden;
height: 100vh;
}