Why is the Zabur a divine book that mentions neither a nation nor followers, and why are there said to be three religions and not four?

All the expressions mentioned are correct. The Zabur is a book that Allah revealed to His Prophet Dawud (peace be upon him), who was one of the messengers of the Children of Israel. The Zabur did not contain jurisprudential rulings; rather, it consisted of admonitions and wisdom. The nation of the Children of Israel worshipped with it during the era of Dawud (peace be upon him), along with the rulings of the Torah.