I think there might be more to it. While it might just be me, I think Kagi could use some improvement here. I've been using Kagi with Safari on Mac for about a year, and never got the search extension to work consistently. It would sometimes give me Google, and sometimes Kagi. And sometimes it would give me one site then switch to the other after a several second delay.

Eventually I gave up and uninstalled their extension. I switched to using StopTheMadness to do the redirects instead, and am having much better luck. I did switch from redirecting Google to redirecting Ecosia at the same time, and this might be the difference, and while I'd fully agree that Safari doesn't make it easy, but I think the base problem is that their browser extension just doesn't work that well.

(If you are familiar with both, you will understand that switching _to_ StopTheMadness for a better interface is pretty high in irony!)