This is a limitation implemented by Apple/Safari. You can only choose a default from the list they provided (Safari --> Preferences —> Search --> Search engine). The closest you can get in Safari is to perform a search on search.brave.com, then you can use the Safari “quick search” option to search using Brave via the address bar. Simply start typing in search.brave.com until it auto-populates, then hit Tab then enter your search query
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