I never liked Brave. Some years ago I installed Brave on my Linux desktop PC and there were things that I didn't like compared to Mozilla Firefox. On my android smartphone I first had Firefox and six months ago (or so) I switched to (Firefox) Focus. Focus also comes out good as a private browser, I see. By the way it's already Focus version 126.0 in the meantime.

Vivaldi (which I really like on the desktop and on iOS (I don't use Android), though they do occasionally release poorly tested versions that have major problems), has several settings related to cookies, including ability to restrict them generally and globally to session cookies or to block them entirely, as well as separate controls for "third-party cookies", which can be blocked as well. I suspect more restrictive choices for these settings would bring it in line with Brave. However the so-called "user experience" would suffer as a result, so depending on how you want to go....