There is no "scammy" behavior in our past. What you're linking to here is an affiliate link offering from pre-search UI in the browser. This involved no user data, no privacy impact, etc. See the official response here (with screenshots, so as to clarify how the feature actually worked): https://brave.com/referral-codes-in-suggested-sites/.
If an affiliate link offering (shown plainly, and prior to any navigation event) worries you, wait until you see what other browsers are getting away with. If you're using Chrome, Edge, or Firefox, your browser serves as an out-of-the-box keylogger, sending each keystroke off to Google (Chrome and Firefox) or Bing (Edge) as you type into the address bar. Even an unintentional pasting of sensitive information gets transmitted.
If an affiliate link offering (shown plainly, and prior to any navigation event) worries you, wait until you see what other browsers are getting away with. If you're using Chrome, Edge, or Firefox, your browser serves as an out-of-the-box keylogger, sending each keystroke off to Google (Chrome and Firefox) or Bing (Edge) as you type into the address bar. Even an unintentional pasting of sensitive information gets transmitted.