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It means that it works the same way that first party cookies already work. HN can't see my Google cookies and vice versa. If I clear my cookies Google has no way to know (aside from fingerprinting and maybe IP) that I'm the same person.

> What is the use case where you want to connect new session instead of using the old one?

Multiple accounts? Clear cookies and visit the next day? Probably other stuff as well. The import point is that DBSC doesn't itself increase the ability of website operators to track you beyond what they can already do.