I run the browser under different OS user accounts, and make my display manager display the user account in the window title bar.

https://megous.com/dl/tmp/8eaa15e187fa9a2e.png (ff1 being the user)

I trust it more than browser's internal isolation solutions, like tab containers, which I like to use for other things, like testing web apps using different login sessions at once.

I'd hate a remote solution. ;) Though this is not for privacy but more for protection and better low effort isolation.