I was linked https://lite.duckduckgo.com/lite, and even without autocomplete or dropdown functionality, it comes in at 8.5 kB, so I'd say that the 10 kB goal is pretty aggressive.
That seems unfair, considering there is no lite google equivalent. The full duckduckgo site still comes in lighter (3/4 of the size), and includes a lot more media, so it's still better than Google.
Autocomplete function, dropdown menu JS, 10kb max
Considering this page is viewed by millions, and doesn't even contain the logic to render search results