On June 12th, I did three complex Kagi Assistant queries. Only 1 search is listed in my account usage (consumption) page.

By just roughly counting up the number of bullet point searches in my assistant text under "Searched by Kagi", I see more than 10 in each Assistant query.
I expect the total number of searches to go up in my account consumption page based on assistant usage.
The "i" info box should also show the total number of searches used for that query.