Which version do search engines crawl?

Which version search engine will crawl depends on the conditions you use and the order they are set in the trigger. Google and other search engines crawl the web stateless, i.e. without cookies. This is something Google has said many times over the years., the page Search For example, if you set a “New visitor” condition, search engines will see the content as if the condition was met. If you’ll set a log-in condition, search engines will not see that content. If you set a “Dynamic link” condition – search engines will treat it like another page (you can set a canonical if you want).

The important thing is that search engines will always see the same content.

You can learn more about dynamic content and SEO here:
https://www.if-so.com/dynamic-content-impact-on-seo/