I quickly downloaded the kagi extension for testing and there I can see the leaking - the Qwant extension still does not leak. Maybe you could also test the Qwant extension?
I did: https://news.ycombinator.com/item?id=43175181
There's really no magic or mystery here. The extension is simply using this API: <https://developer.apple.com/documentation/safariservices/sfs...>