Your screenshots are not displaying, however, the default live search functionality in Magento 2 does not have any search hinting or predictive suggestions capabilities. It only provides the dynamic dropdown showing matching search results.
However, extensions like Amasty Predictive Search, Mirasvit Sphinx Search, or Lucidlane Predictive Search from the Magento Marketplace can add search prompt hints and term recommendations on top of standard live search.
These plugins work by indexing catalog data and leveraging analytics to power algorithms that predict what customers intend to search for based on initial typed characters. The hints then augment the default instant search dropdowns.
