Surely Baez's even in American English (yeah, I know it's a Spanish name).

British English almost always adds 's for the singular possessive, even when the name ends in s, so Dickens's and St. James's.

However, American English often uses the plural possessive suffix ' for names ending in s. One Spanish name example I have seen is Bezos' for something of Jeff's (his billions, or his wives, I forget which).

But Baez' makes no sense to me on any side of the Atlantic.