If he were to go around saying, as you put it, that he “was appointed by God,” he wouldn’t just be hinting at personal belief, he’d be stating it as fact, and that would quickly become a far bigger issue than his private faith. He cannot claim divine appointment as a basis for authority; his power comes from Parliament and the constitution. History makes that clear. The last king to insist on divine right was removed from the throne, and his predecessor paid for it with his life.
I agree that when people express their faith publicly, it reflects devotion and belief in God. But praying, taking oaths, or showing reverence (like kissing the Bible) are acts of faith and solemnity, not declarations of divine appointment. They show personal belief, not a claim to authority granted by God. Do you apply that interpretation only to the royal family, or to all Christians?
As for William (or anyone else’s personal beliefs) I’ll leave it with Elizabeth I (who was also the first to use the title of Supreme Governor of the Church of England): “I have no desire to make windows into men’s souls”. We shouldn’t be policing private thoughts and beliefs.