Vlad from Kagi here.
We are in the process of rewriting our Safari extension for Kagi search, which proved to be very challanging (Apple seems to really not want people doint this). It is open-source and you can check the discussion here [1]
Our current extension should mostly work though (maybe needs full reinstall) [2]
We also launched Orion browser on both macOS and iOS which is made as a Safari replacement and comes with Kagi integrated. [3]
Finally, there are third party extensions that you can use like xSearch [4] and HyperWeb [5].
Do not forget to move Apple in the right direction to allow use of custom search engines by sending feedback [6]
[1] https://github.com/kagisearch/browser_extensions/pull/59
[2] https://apps.apple.com/us/app/kagi-search-for-safari/id16228...
[3] https://kagi.com/orion
[4] https://apps.apple.com/us/app/xsearch-for-safari/id157990206...
[5] https://apps.apple.com/us/app/hyperweb/id1581824571
[6] https://developer.apple.com/bug-reporting/