“I wonder if they will be granted universal citizenship?”
Nations will need to make laws that human children born in space carry the citizenship of their human biological parents.
However, many nations today, including the U.S. allow for “dual citizenship” - citizen simultaneously with two nations (yes, U.S. law has never prohibited it for U.S. citizens).
Should humans have actual living/working self-governed off-world settlements, human laws will have to reconsider the citizenship issue, to permit, or deny, dual citizenship with human off-world domains.