Interesting, so would Safari prevent this? I tried moving to Safari and honestly loved everything except I use my google accounts now for authenticating with to many services and that was a pain compared to chrome.
I honestly kind of forget the exact annoyances because it has been some time. I want to say I had to reauth every time I wanted to SSO with my google account because it doesn't allow/deletes third party cookies.
Chrome for some reason (still!) gives extensions static ids. Firefox has the id change per firefox instance.