I was just checking the instructions at this page https://help.kagi.com/kagi/getting-started/setting-default.html#chromium_desktop
in particular the screenshot:
following the instructions on Chrome 125.0.6422.77 (Official Build) (arm64) doesn't make the above to appear, but I get this instead:
Kagi is only present in Site Search and not in alternative search engines.
For this reason it's not possible to customise the Search Engine in latest Chrome.