Thanks. So it appears that most of it is separated, with the exception of web history and search and form data (which can be identifying). This was also interesting:

"Users can log into multiple accounts on the same site, even when the site does not natively support concurrent sessions. ... Current solutions: Users open multiple browsers (this takes users away from Firefox). A user opens one account in Private Browsing mode (this has a limit of 2 accounts, and forces one to be ephemeral)."

There is no mention here of the -no-remote flag which has been available for many years.