Why does my site read hot for search and cold for AI?

Because those are different problems and the second one is newer. A site built carefully in 2019 routinely reads in the eighties for Search Visibility and the forties for AI Discoverability, and nothing it did wrong was wrong when it was built.

The usual causes are a robots.txt written before AI crawlers existed, content assembled in the browser rather than sent by the server, and no self-contained answer near the top of any page. All three are fixable and none of them affect classic search.