I knew Kagi was essentially a meta-search provider (they use lots of indexes to try and produce a more accurate search result), but wasn't aware they use a SERP provider with Google results. Uruky does and it seems to be offered upfront for users that want a more Google-like experience. I'm wondering where you found that out?
They say "our search results also include anonymized API calls to all major search result providers worldwide": https://help.kagi.com/kagi/search-details/search-sources.htm...
Google of course does not have a search API - Kagi is paying (IMO sketchy) SERP scrapers for these results. One of the reasons I canceled my subscription
If you take them at their word, they would love to be able to pay Google directly for such an API. But I think it would take a government requiring it for Google to do it.