Yes, without linking to a specific client, with a neutral visualization like njump.me It would be cool if you also expose a relay with search capabilities (https://github.com/nostr-protocol/nips/blob/master/50.md). One more, maybe crazy idea: this search relay could also return generic web results* through notes generated and signed by Kagi, so users could search the web within their preferred Nostr client, share and comment results. Of course this would give Kagi a nice visibility. * Only when the filter set Kagi as author.

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Bonus for your final crazy idea: eventually the Kagi web search results would function as a Nostr-based timestamped archive of search results across the web. You could view the history as "what links and page previews did 'search term X' return on 6 date in history". Even better (and crazier) of the pages themselves were converted to markdown and saved as events...