It may be challenging to find a specific case study solely focused on nofollow backlinks used in SEO and digital marketing, but you can check a few factors that instruct search engines not to pass authority or page rank to the linked page:

You can consider these:

• Google's Official Statement: Google has said that nofollow links are normally not used for ranking considerations. Search engines may still crawl and index them, though.
• User Experience and Traffic: While nofollow links do not directly affect search engine results, they can nevertheless drive traffic to your site if visitors click on them. Increased visitors might indirectly improve your website's exposure.
• Natural Link Profile: A diversified link profile that contains both nofollow and dofollow connections is considered natural by search engines. It may imply that your website is not attempting to influence search rankings.
• Social Signals: Links from social media platforms are frequently nofollow, but they can help enhance exposure, brand recognition, and referral traffic.