[Straight Vermonter]

...just as in Istanbul there’s still a building called St. Sophia’s Cathedral

Oops. I suspect he is referring to the Hagia Sophia which mean "holy wisdom" not St Sophia.

[Question_Assumptions]

I've seen it referred to as "St. Sophia" in more than a few English sources, though you are correct that it's properly called "Hagia Sophia". I write it off as one of those things like talking about the "dead presidents" on US paper money, even though the guys on two of the more common bills ($10 and $100) were never presidents.

[Antoninus]

Oops. I suspect he is referring to the Hagia Sophia which mean "holy wisdom" not St Sophia.
St. Sophia is another name for it, as in "Sancta Sophia" which is the Latin equivalent of Hagia Sophia.