My guess is that there are Muggleborn students at Hogwarts against the orders of the regime, and the book would contain records of who they are.

Because someone took the Swithin girl's place -- possibly in a wizarding family who are raising the child as their own -- and there are still records of the kid's biological parentage kept at Hogwarts.

So, more concisely, my guess is that 'the book' is a record of all children enrolled at Hogwarts, and possibly magically updated so it might have more information available than that known to the Lord Protector and his government.