Kagi has an extension to add itself. https://help.kagi.com/kagi/getting-started/setting-default/s...

This is what I used, but it’s a bit of a hack. It has to hijack one of the other search engine, which then becomes unusable. It also doesn’t show the search term in the address bar, like the person was asking for.

You can thank Apple for that, presumably because they receive a ton of money from Google.

Google isn’t the only option in the list.

And of course it’s Apple’s fault, they wrote Safari. I submitted a feature request a while ago, but I’m guessing more people need to do the same.