"As overlays do not modify the original source code or semantic structure of the website, they just add a new layer on top, the overlay cannot reliably fix these core problems for screen readers or other assistive technologies.", and interesting article by Chris Yoong on how and why German auditors reject accessibility overlays in EAA context.
https://chrisyoong.com/blog/germany-rejects-accessibility-overlays-for-eaa-compliance
https://chrisyoong.com/blog/germany-rejects-accessibility-overlays-for-eaa-compliance