Following up on #10145, we should determine whether elements can define a view-transition-class inside shadow DOM that gets matched to a corresponding class in the pseudo-element (e.g. if the element is a ::part)..
Based on https://drafts.csswg.org/css-scoping-1/#shadow-names, I think it makes sense to allow that, as a view-transition-class is similar to giving an element a font-family that's defined in the root inside a @font-face.