Amazon has updated the stock browser on their Kindle devices in late 2023, making the browser usable and good on even ancient Kindles.
After logging in to Kagi it is possible to use the search, but no results are displayed for any search query. The rest of the Kagi UI shows.
I expected search results to be displayed. The Kindle browser is after the update good enough to use modern websites. For example, you can use Fastmail without any issues.