Both on kagi.com and using the API directly, queries that one would definitely expect to return autosuggest results return no results.
My test queries were "ghee vs", "australia ", "bananas ", and "1 + 1" which absolutely would have got a result in the past.
kagi.com uses https://kagi.com/autosuggest?q=, which returns an empty JSON list, watching the network tab in devtools as I type.
The documentation recommends https://kagi.com/api/autosuggest?q= on a phone / manually configuring an engine, which returns ["the text of the query", []] for all results.
Autosuggest used to work. It wasn't amazing, but it did return results.