wouldn't they know exactly who you are with every request sent to any of their servers and any facebook page you load either by your facebook account, IP address, or by browser fingerprinting.
But in another very real sense they've got no idea who that is. It would suit them very well to be able to reliably tie it to other information (hence all the tracking pixels and so on) but the Container prevents that.
I mean, one of my Facebook friends is named say "Norman Le Plum". I'm very confident that isn't what it says on his birth certificate, and indeed when his friend request arrived I actually ignored it until I found someone out of band to tell me who "Norman" was, but in a sense Facebook know exactly who Norman is, he's a disembodied red skull who is still really into skateboarding and Steamed Hams.
What use that is,isn't clear, and presumably one day advertisers might conclude the answer is "No use whatsoever" and Facebook will go out of business. Meanwhile I read funny Steamed Hams variants, people complain about their jobs, and while I'd rather it didn't exist at all, if it must exist at least it's trapped in a little box where it can't taint everything else.
Now Google probably knows way too much about me, but that's quite a different problem.
Facebook devotes a huge amount of time and money to collecting data and using it to associate people to a real identity to the extent that even people who never signed up for an account at all have hidden profiles created for them by facebook which contain the intimate details of their life including what they buy at the grocery store.
As far as I can tell, a container won't protect your identity but it will limit the amount of information they have on your browsing history (unless your ISP decides to sell them that information or they obtain some of it from a 3rd party data broker)
But yes, in a Foo container, all the various Google things (Docs, GMail, their Cloud offering, Youtube...) are either not logged in at all or they're logged in from some Foo context.
e.g. I have that Facebook Container, and I also have a Slack container I just put together in the usual way by opening my Slack session (it's for the main social group I hang out with, during the pandemic) inside a Container with a pink theme and icon.
Suppose three friends send me a funny Youtube video of kittens, one sends it on Slack, one on Facebook, one literally sends me a postcard with the URL on it.
In Facebook, it's inside the Facebook container. Since the Facebook Container has no idea who I am, Youtube presents adverts and of course there's no way to add the video to my "Fun kitten videos" list. But if I tell Youtube to open this now the tab is not Facebook, a no-referrer link opens with the URL and now in my default context which has Youtube Premium, so there are no adverts and I can add this to my lists. As far as Facebook is concerned I apparently just left. Unless Google tells them I watched that video they are none the wiser.
Slack is inside the Slack container. So again, no Youtube account, adverts. But if I open the Youtube page that's still inside the Slack container, so still no Youtube account. I need to explicitly get the URL and paste it into a not Slack tab to get my default context.
The link from the postcard obviously I get to choose which context to type it into the URL bar, although maybe the UX of typing random Youtube URLs in isn't great.