I normally do not save browsing hisroty and cannot turn that off. I can empty it, but cannot stop it.
Same for search.
I could do all of these things on the pre update brave.
I tried and wanted to support Brave but never liked how it worked - similar to what youve been seeing (Im sure theres a buried menu option to set the homepage)
Been using Pale Moon instead.
I did just figure out how to get my home page.