So far the Brave Search product is really excellent, well done all!
I would ask that on scrolling up the searchbar is shown, or perhaps when scrolling down show a scroll-to-top button.
Currently, in order to modify your search, or run a new search, you must scroll all the way to the top of the page. This can take some time if you are quite a ways down, especially on mobile.
I did not see this feedback/request anywhere, but I may have missed it–apologies if this is a duplicate.