We don't put any popups anywhere by default. Are you sure the website wasn't trying, which flies a permission prompt same as in Chrome and other browsers?
I turned on the special, approved Brave ads thing last time I used it because I wanted to support Brave; and they only showed up as little pop ups on the systray and were infinitely more annoying to me than a static banner ad.
You click on them to open new tab pages if interested, can thumbs down and lower frequency in ads settings. You also get 70% of the sponsored images shown in 1 of 4 new tab pages. Static banner isn’t going to perform as well, so I hope you will give ads a try again. You could even turn off notifications but keep the sponsored images.