This is what Firefox containers really helps with. Check Add-ons - it's a Mozilla created one. Containers were a larger form of the Cookie Jar and really useful for managing multiple accounts on the same site. Cookies saved for one account persist only inside that container.Firefox starts up so slow for me compared to Chrome or Edge (on a PC).
You just made me think about the most irritating thing I deal with -- Microsoft sites. It's frustrating trying to actually log out of a MS site (O365 Admin Center for instance) and log in with another account because it always seems to remember! Let alone, logging into 3 tabs of M365 under 3 different accounts, which is impossible.
I just tried it with Firefox 86.0 and it works fantastically! Finally, I can log in as who I want at MS sites without having to play games trying to get it to forget the last account I logged in as (or using Incognito windows).
This latest just takes it one step further and firewalls websites inside a given container.