Brave have announced a new feature coming to their web and Android versions, known as Forgetful Browsing
Forgetful Browsing the global default, you can type in brave://settings/shields in the URL bar and toggle the Forget me when I close a site option. You can then make exceptions as mentioned above by tapping the Shields icon in the address bar -> Advanced controls and disabling the Forget me when I close this site toggle(version 1.53 on the web and version 1.54 on Android)