The Quote from the FAQ explicity says "anonymized API calls". This is obviously mean that they use official API provided by these providers. And that is part of the reason why they have some high per search cost they have to cover.

Assuming they use some form of this Google API[^1], they're surely paying for the results. What bothers me is that, by paying for Kagi then, part of that monthly fee is going straight back to Google, right?

[^1]: https://developers.google.com/custom-search/v1/overview

They are business partners with Google.

Google’s entire business is based on scraping stuff no-one asked them to so they can go fuck themselves if they don’t like it. The same applies to Facebook. The gall of these companies trying to “ban” public web scraping when they’re the prime movers in that domain is quite something.