I was also annoyed by the fact that the advanced search isn't available directly on the home page. It should be a feature that Kagi makes front and center, and there's a lot of empty space on the home page.
But I was quite confused seeing this post because my UI doesn't look the same at all. I'm using Opera for Android, if that matters.
Screen recording:
https://kagifeedback.org/assets/files/2025-04-26/1745670905-130970-screenrecorder-20250426-083203.3gp
Another annoyance is the fact that the advanced search doesn't populate the fields with what you wrote in your existing query.