What I'd like is a Mullvad container in regular Firefox so I can choose what sites to open in it, or rather make it the default and move a site to another container if I want permanent cookies. I use temporary containers now but the extra fingerprinting features appeal to me.
Your browser can still be fingerprinted without cookies. The site just needs enough unique information (user agent, timezone, screen size, IP, operating system, country, etc.) to form a trackable identity.
This is a surprisingly effective one when combined with other users of your network. A couple of years ago, I started getting Facebook ads for things I'd never looked at, but that I knew my wife had looked at. We don't share any devices, and she doesn't even have a Facebook account.
It's pretty troubling how invasive shadow profiles are.
My understanding is that cookies etc aren't shared between containers, so I can stay logged in, and not be tracked across websites.
If it's achievable, why compromise?