Help Needed: Rich Text Nesting Disconnects When Pasting A Component Across Projects

Hey everyone! I have a component library within my app, and I was wanting to add a new component that allows people to copy & paste a blog page with a rich text element into their Webflow project. I styled each text element ‘when nested inside of’ the rich text element. But when I paste this component into another project, the nested inside of link breaks, and reverts to Webflow’s default styling for the element. Video below.

When I paste the rich text element by itself there is no issue… I managed to get this to work for another component, but can’t quite figure our what’s wrong here.

Does anyone have any ideas on how to fix this?