From my tests Kagi will show the translate widget if I query "translate", but not when using "translate <word> to <language>", or "translate <word> from <language> to <language>". The expanded forms of the query have the information to populate the translation fields to immediately get the result to the user. "translate <word/sentence>" could also default to translating to the user's interface language.
The widget ocasionally gets filled with the second form of the query if it was already up from "translate" but I couldn't figure out what makes that work.
I was used to doing this on Google, it allows you to directly do things from your search bar or inline with searching instead of context switching to the fuller translate page, or with a search outside of browser that then opens up kagi's page.
