This is a new take on what boosts visibility in AI tools (at least to me) - according to Dan Taylor, data from 2138 websites cited in AI search shows a correlation between CWV performance & visibility in generative answers:

• Sites with CLS ≤ 0.1 recorded a 29.8% higher inclusion rate in generative summaries compared with sites above this threshold.
• Pages delivering LCP ≤ 2.5 seconds were 1.47 times more likely to appear in AI outputs than slower pages.
• Crawlers abandoned requests for 18% of pages larger than 1 MB of HTML, highlighting the need for lean markup.
• TTFB under 200 ms correlated with a 22% increase in citation density, particularly when paired with robust caching strategies.

Lots more in the study linked above - plus at the end he offers to share the full deck if you email and ask for it.