A conversion-optimized landing page wants one message, one action, and no distractions. It strips navigation, removes outbound links, and says only what is needed to move the visitor from doubt to action. That is exactly what makes it convert.
A search-optimized page wants depth: enough content for Google to understand the topic, internal links for crawlability, a navigation structure that signals site hierarchy, and a title and meta description written for the search result, not just the visitor. That is exactly what makes it rank.
The apparent conflict is real but not total. Most of it dissolves when you separate the things that help both (intent match, page speed, one clear H1, structured data) from the things that genuinely trade off (navigation links, content length, outbound exits). The trick is knowing which is which.