rem units always inherit from the document root (), not the Shadow DOM. To prevent font-size inconsistencies across sites, the best approach is to either:

Use transform: scale() to normalize font scaling inside the Shadow DOM based on the page's root font-size, or

Use an for full isolation and root control (especially useful for overlays or popups).

Overriding UI library styles from rem to em or px is possible but impractical unless you're customizing the entire theme.