I found this exact bug today also on my Android device. Kagi seems to respect the search suggestions setting in my Windows desktop at home (Firefox), Windows desktop at work (Edge), and even when running Kagi inside the Firefox browser on the very same Android smartphone where I also have the Kagi app installed.
On the Kagi app, however, search suggestions show up still. I have confirmed that I am correctly logged in there and that when visiting the settings page through the app, it correctly reports search suggestions as disabled.
As of now I am not using the Kagi dedicated app except for Assistant due to this very bug, I find search suggestions too distracting. As a workaround I have been using Kagi inside the Firefox mobile browser.