Like discussed on the "ai" channel on discord, it seems like that the current "path" will be : search => select a result => ask summarize.
For my usage, i don't see me ask for a summary of an article who i don't know the size/ form, because it cost me "credit", the summary could be useless, so I would : search => select a result => check the result, see if a summary is useful => get back on kagi => ask for a summary, it seems pretty heavy.
It could be useful to add the summarizer in the extension of kagi, it would give : search => select a result => check the result, see if summary is useful => ask a summary, from the extension, without leaving the article. Think it could help for the user experience and help to get the best usage for summary. Get the summary result in the extension would be nice, but i doesn't tested the tool and don't know if it would fit.
Because the ask question is on a single document too, it could be added in the extension too, without leaving the article, so I could read it, and ask more, from the extension, without leaving the text and images of the article.
It could be set as two options, a first button "Summarize" and an input box "Ask anything from this page".