Especially when I have not searched from the URL bar in a while, if I search for new terms in Safari and hit enter, the page of what is defined as my Safari "Default Search Engine" loads up with that search for a split second before I get redirected to Kagi. This means my searches get leaked to (Google, Ecosia, Bing, DuckDuckGo etc). I tried switching the extension from redirecting only one site to all search engines, made no difference.
Quite hard to replicate but on a future morning when I have not searched for a few hours on my desktop I will try to record the screen.
Latest Safari on macOS 26.5.2, Kagi for Safari 2.2.3
Expect the search to go ONLY to Kagi and never leak my searches to the search engine Safari would like to use if it wasn't for the extension.