I like to use a combination of Brave and Kagi searches, however on iOS you can't install your own search engines. This article describes how I managed to set up search behavior in Safari on iOS to my own liking.
window.stop();
document.body.innerHTML = "";
var w = ((/q=([^&#=]*)/.exec(window.location.search))[1]).split("+");
if (w[0] === "k") {
w.shift();
window.location.replace("https://kagi.com/search?q=" + w.join("+"));
} else {
window.location.replace("https://search.brave.com/search?q=" + w.join("+"));
}
var swke = document.getElementById("searchWithKagi");
if (!swke) {
var q = /q=([^&#=]*)/.exec(window.location.search)[1];
var body = document.getElementsByTagName("body")[0];
var kagi = document.createElement("div");
var link = document.createElement("a");
link.href = "https://kagi.com/search?q=" + q;
link.innerHTML = "Search with Kagi";
kagi.appendChild(link);
kagi.style.background = "yellow";
kagi.style.textAlign = "center";
kagi.style.padding = "10px";
kagi.id = "searchWithKagi";
body.insertBefore(kagi, body.firstChild);
}
You should be good to go now.