So, like the title says I'm pretty sure that AdSense's GDPR modal is what is causing the layout shift on at least one of my websites. And this in turn means the site fails on Core Web Vitals.
When I run the Lighthouse tool via Chrome it sails through - because it isn't rendering the Funding Choices pop up. Running it through the PageSpeed Insights all I get is a bunch of thumbnails of the Funding Choices overlay.