When searching for "when is lunar new year", I get these results across Kagi's different modes:
Main search: no date provided. The top link is good (Wikipedia), but it requires clicking through and scrolling down to the table to get the answer.
Quick answer: Incorrect. States that it is Jan 21.
Expert assistant: CORRECT. February 10. Also gives some amusing stats from Wolfram Alpha. Good result.
Fast assistant: Incorrect. States Jan 22.
FastGPT: CORRECT. This is easily the best response of the bunch: it has the right answer, and provides meaningful context about what Lunar New Year is. It also provides 5 high-quality links. Excellent result.
For comparison: on Google, the correct answer is embedded in the search, with the date highlighted. I consider Google's answer to be slightly worse than FastGPT but much better than Kagi's other results.
Here are screenshots of all my results:
Ideally, all modes would return the correct answer within the first sentence, in an info box, or at least visible in the result snippets or Wikipedia sidebar preview.
For bonus points, including the Chinese Zodiac animal like Google does would be useful.
Obviously, incorrect dates should not be returned.
For comparison, searching for "when is easter 2024" gives me an excellent instant result: 
