It isn’t chicken pox that protected people from small pox. It is cow pox.
I had chickenpox as a child,along with almost everyone else my age, and was forever asked about it, and assumed, obviously wrongly, that it immunized one against deadly smallpox.
Different diseases. Smallpox was eradicated, and it's best we all clearly know that they are not related, and that nobody labors under the false assumption they are immune.
Thankfully, I did decide to inoculate my child against chickenpox, when it was an optional vaccination.
That was several years before I developed shingles myself.