Thanks, it seems firefox has the same feature on the padlock. Otherwise, from the other comments here, I might be able to try one of these two to help in conjunction with containers:

https://addons.mozilla.org/en-US/firefox/addon/cookie-autode... https://addons.mozilla.org/en-US/firefox/addon/session-boss/

I can't switch to Chrome since I can't live without tree style tabs anymore. I've become dependent.