Additionally to the other two replies, Brave also injected referral IDs to an URI when you directly typed it in. Allegedly it was a mistake and they put it behind a toggle:

• Article: technewsworld.com/…/brave-browser-caught-redirect…
• Their blog: brave.com/…/referral-codes-in-suggested-sites/

Also, per default the new tab page shows advertisements in the background. Firefox does also show ads on the new tab page in the link grid, so it’s a bad thing both do and you can disable it on both. But with an almost-full-window sized ad Brave managed to make that worse still.