I took a closer look and the iOS extension supports entering a “session link” which allows the Kagi redirect to work in private windows. Entering it is a bit cumbersome—you have to first open a private window and then any random page so you can see the extension button in the address bar, at which point you can tap it and then the Kagi icon to get to the session link field—but it appears to stick after that and the redirect works as expected (although you do get a brief flash of Google or whatever — they suggest changing it to DDG which looks a bit smoother).
Agree that it feels hacky, but sometimes you just have to take what you can get.
I realize this is probably not the solution you want, but there is an official iOS Safari extension that will intercept all address bar searches and route them to Kagi. I don’t remember how much it costs, and it doesn’t seem to work super well with private browsing, but it’s better than nothing and works well for what it is. Ymmv
You spelled "misspelled" correctly, which earns a point in my book because (in a profound display of irony) a lot of native speakers misspell that one!
Am I literally the only person who sees the pun against “His Girl Friday?” Maybe it wasn’t intentional but that’s literally the first thing I thought of.
Seconding this comment. I grumbled at first about paying for it but frankly after more than a year I’ve come to realize it’s money well spent considering how much use my family gets out of it.