I don't use any of these "log in with ..." things, as I create a new email address for every service. However, what you'd do is put each site that you "log in with ..." into the same container, so that they can share cookies.Does this mean everytime you want to use a 3rd party tool like "Sign-In with GitHub" you're going to have to relogin to that 3rd party tool to get new cookies? (Which for people who use FIDO auth means having to drag out the USB dongle again)
If so then this is just going to suck.
So you'd put GitHub into a container and then when you connect to a service that uses that log in, just open it in your "github" container.