Every time I close [completely] my browser on my MAC Big Sur [11.2.3] I feel that I lose all my cookies, seems the browser is cleaning it even though I don’t have this setting enable. It happens to all the websites not only Google ish… I’m Running Brave 1.24.82 version
I receive the page to consent google every time, like the one below
go to brave://settings/clearBrowserData and make sure you did not select anything on the exit tab
go to brave://settings/cookies and make sure you did not turned this on Clear cookies and site data when you quit Brave
if both was fine then could you disable all extension and try again and if it work then reenable them back one by one till you get the one that cause the issue
some extension clear the cache and other could corrupt it especially if there browser update that could make some extension not compatible with that new version
so disable it to make sure that nothing outside the browser has affect on it
so give it a try and let us see how it going