Edge in Windows 10 will not allow seach.brave.com to be selected as default browser even when added to Manage search engines. It does not appear as a choice although google etc. are all listed as choices
https://search.brave.com/
@ken3491phillips Hi and welcome to the community. 
Do you have Brave up at the same time as Edge? If I have both up at the same time, the settings I try to make in Edge did not work for some reason. If I close both browsers, then open just Edge, I can make the changes and then they will work, even if both browsers are open. Not sure why, it just did.
Edit: Oh, want to add, I am using Brave version 1.36.112, not Beta.
Just saw this in another post. Thought you might be interested. I did not use this string but mine worked anyway. Going to go see later if it makes a difference in anything.
https://community.brave.com/t/brave-search-in-non-beta-brave-brower/357379/2?u=chocoholic