You are stripping the Referrer from being available on the landing page when a user clicks through from Kagi. I expect this is a misguided attempt to preserve privacy: it does this, in particular masking the search terms used on the search, it means site owners don't recognise the visitor as arriving from organic search and won't have any idea of the market size of Kagi, hence no incentive to make sure they index well there.
You can mask the query parameters while still showing your origin, in ways similar to how google does this. This should balance privacy with accurate attribution of source.
Happy to test if you want to do this.
- Type search term into Kagi and search
- Click through on a result
- view
document.referrer
and see it is an empty string