I’m also having this problem with Kagi and the Userscripts extension. For me, it manifests as my search term being changed to the previous thing I searched for. For example, if I search “cows” using the address bar and then later search “pigs” in the address bar, the Kagi login page flashes, then I quickly am shown the search results for “cows”. (It’s not just the results, the whole page acts like I searched for “cows”.)
Weirdly, I only have the Userscripts extension enabled for a few pages (none of which are Kagi or the placeholder search provider, DuckDuckGo), and the Kagi extension is also only enabled for DDG and Kagi.com. They should never be running on the same page.
This is Kagi extension v2.2.8, Safari in iOS 26.0, with DuckDuckGo as my placeholder search engine.