To exclude content from AI overviews and snippet (ex: meta description) in the SERP, you can provide a nosnippet meta tag. If you want to exclude some part of the webpage from the SERP, you can request crawlers to exclude it by a data-no-snippet tag.
Data-nosnippet only works on <div>, <span> and <section> HTML elements. It’s a boolean attribute so when it exists, it always means true, even if you add data-nosnippet=false attribute. The div, span or section must be closed, otherwise everything after the no-snippet will not be shown.
Here’s a test by Glenn Gabe where you can see this in action: https://www.gsqi.com/marketing-blog/how-to-remove-content-and-links-from-google-ai-overviews/
GSQI
Recommended Reading
a. https://developers.google.com/search/docs/crawling-indexing/robots-meta-tag#nosnippet