I am relatively new to Brave (on Windows 10), and there are two unanticipated privacy issues I have identified.
Brave apparently saves the sites that have been visited in private tabs. I found this when the ‘most visited’ sites were suddenly listed on the starting tab (non-private), which is highly disturbing and the exact opposite of what one would want and expect. I assume that even if one simply unchecks the option to display top sites on new tabs, they are still stored somewhere and pose a privacy risk.
Recently I was about to type something into a search box on a website and was shocked to find that there were several words autosuggested that I had NEVER typed in any Brave tab or window before. I know this because they were all related to a specific project I was working on and completed some months before I even downloaded the Brave browser. So it seems Brave is harvesting search histories from other browsers on my computer, which is very far from private.
For these and other reasons, I will be uninstalling Brave because it seems it compromises your privacy even more than some other browsers out there.