Yes brave://settings/content/cookies and adding google.com to the Clear on exit list and Google.com is in the Clear On Exit.
No I do not have the option Clear cookies and site data when I quit Brave toggled “on”. If I do enable that then Brave deletes 2FA cookies for other sites like Discord and Reddit and it also takes out cookies for services that use my Google account like Feedly, YouTube settings cookies when I exit Brave. The last time I tried Clear cookies and site data when I quit Brave toggled “on”, I still remained logged into Gmail when I started Brave back up! Reddit, Feedly and Discord are NOT on the Clear on Exit list.
Yet when I go to “brave://settings/siteData?search=cookie” scroll down to the line with Google.com
and hit the garbage can on the line for Google.com and its 15 cookies so that ONLY those 15 cookies are deleted and then go over to my Gmail tabs and reload the Gmail tab I find myself logged out like I should.