"But it's explicitly stated to be a consequence of a saying that "cannot fail of its effect".
Look again:
"And since that saying of our lord Jesus Christ, "You are Peter, and upon this rock I will build my Church," cannot fail of its effect, the words spoken are confirmed by their consequences."
The statement that "cannot fail of its effect" is "You are Peter, and upon this rock I will build my Church."
"No, the Catholic faith is always the same."
Really? What happened to extra ecclesiam nulla salus?
Yeah. That's the statement. Its effect is that "in the Apostolic See the Catholic religion has always been preserved unblemished, and sacred doctrine been held in honor".
... since that saying of our lord Jesus Christ, You are Peter, and upon this rock I will build my Church, cannot fail of its effect, the words spoken are confirmed by their consequences. For in the Apostolic See the Catholic religion has always been preserved unblemished, and sacred doctrine been held in honor.
Looks like a pretty clear causal connection to me.
What happened to extra ecclesiam nulla salus?
You tell me. I'm not aware of anything having happened to it.