He’s chosen the name King Charles III, third time lucky with that name. As in not a taig. Though the “defender of the faiths” thing is worrying.
You have to look at the plural there mate, Faiths, He is tasked with defending the rights of all faiths equally regardless of his own very much like most religious leaders.
The Faiths are CoE and the CoS and Presbyterianism in Scotland. He isn't the defender of any else especially not the Catholic cult. And rightly so.
All faiths include Baha'i, Buddhism, Christianity, Confucianism, Hinduism, Islam, Jainism, Judaism, Shinto, Sikhism, Taoism,Trekkies and Zoroastrianism,imho.