When at https://search.brave.com/, hitting the enter key in the search box enters a carriage return instead… of actually performing a search. The search box in the search results page behaves as expected.
As an alternative, I would press tab to change focus to the search icon, except it doesn’t get selected, I can only focus the ‘x’ to clear the search box.
I rather like this search engine, I was surprised the “wanted” behavior wasn’t already coded in. 