is Open at GitHub – today, Monday, Feb. 14, 2022.
Presently in the Brave Browser Settings (Brave Browser 1.35.101 for Mac OS):
there is a switch that is named more precisely:
“Clear cookies and site data when you close all windows”
You have stated that you leave that switch DISABLED (OFF).
And if I may, in my own use of terms . . . you have expressed a wish, that Brave Browser provide selective control over each stored cookie, in order that, you can choose what happens to each cookie – in the event of closing a window and/or exiting (quitting) Brave Browser.
Your objective being, that, with such selective control over the fate of each cookie, with respect to your G-mail account for example, the clearing of some Google cookies, but not other Google cookies, will have all three of the following results:
Upon closing the Brave Browser window(s) or exiting / quitting the application, your Brave Browser would be logged out of your G-mail account, but with a provision:
The 2-Factor-Authentication (“2FA”) Google cookies would remain intact (stored by Brave Browser) - ie NOT cleared - such that:
Upon opening a Brave Browser New Window and going to the G-mail login web page, you ONLY have to use a part of the login process – that is: your G-mail account username and password – while you WOULD NOT have to use the 2-Factor-Authentication (“2FA”) BECAUSE its cookies were NOT cleared, as mentioned.
IN BRIEF, you wish to protect your G-mail account from other people, by using ONLY your G-mail account username and password (and in this login process, avoiding your having to take “2FA” steps), in order to affect your access.
At this moment, my understanding of the Brave Browser, is:
The Brave Browser is a patched (by Brave Software) version of the so-called “Open Source” Chromium browser
Google is taking steps (in Chromium coding) to inhibit the ability – of Brave Software and other organizations that use the so-called “Open Source” Chromium browser – to offer certain functions that benefit such [effectively] Google Chrome competitors
So, I am uncertain about the ability of Brave Browser developers, to establish
Selective Control Over the Fate of Each Stored Cookie
Yet, if you are determined – and you seem to be, despite frustrations with Brave and in your (“snowbound”) life – then forge ahead with your campaign.
PS. When using a Brave Browser New Private Window, cookies do not show in the following Settings page: