Google’s John Mueller said that no, clicks on newsletter emails do not help your SEO or help you rank better in Google Search. He did add that “it’s good to have multiple separate sources of traffic to your website, and not everything needs to have an SEO effect.”
Google may be testing new Google Ads extension icons in the search results. Khushal Bherwani spotted these and notified me of these on Twitter, and I think they are new. New contact us and buy now icons are being placed in the Google search ad snippet.