Unsure if this is now the case — I recall having an exchange via Discord with Kagi's team — but I wanted to formally suggest that when deleting a thread with an in-progress query, that the query is stopped/interrupted the same way it would be when pressing the stop button. See the screen recording below for reference.
I often delete threads with in-progress queries when I realise I no longer need the answer(s) being produced. I find it easier to simply delete it than to find the in-progress query, stop it, and then delete the thread. Saves at least one click and plenty of scrolling.
This would also mitigate against unnecessary token burn, saving costs for users (and Kagi). Particularly relevant when utilising heavily tuned models like Research and Research (Experimental).