Kagi does not use Google's search index. From their post which made the front page of HN yesterday [1]:
> Google does not offer a public search API. The only available path is an ad-syndication bundle with no changes to result presentation - the model Startpage uses. Ad syndication is a non-starter for Kagi’s ad-free subscription model.
They then go on to say that they pay a 3rd party company to scrape Google results (and serve those scraped results to their users). So their search engine is indeed based on unauthorized and uncompensated use of Google's index.
But since they're not using/paying for a supported API but just taking what they want, they indeed are unlikely to be impacted by this API turndown.