Back when I was at school, I actually read the Book of Revelation[0]. I don't see anything that matches it to hard-takeoff — when AI folks talks of gates, it's the logical kind, not what existed when Revelation was written; nothing about seals, final battles, falling stars, imprisoning of seven-headed dragons in bottomless pits, etc. — while I wouldn't be surprised to see some connections (given how little imagination most people show), I just don't see any meaningful connection with any singularity stuff to the eschaton I was raised with.
So, I assume you mean something of a non-Catholic eschaton? And specifically, you have in mind something from a denomination that, regardless of what it says about biblical literalism, doesn't actually pay much attention to what's written in Revelation?
Hard-takeoff only differs from soft-takeoff in the speed of events; given how slow Revelations is ("thousand years" of peace, which I assume was written to mean "a really long time" and not even intended literally), I think that if anything, slow-takeoff is a closer fit than hard-takeoff.
Also, and this is kinda important, the Christian eschaton seems to assume the "good guys" will win[1]. AI-driven singularities just says that some AI — possibly plural, possibly singular — will win, but doesn't tell you anything about the morality of the AI, or if it's a replicated single mind, or a pantheon of different minds. The default assumption from many is more like the Cthulhu Mythos than like anything recognised as a real religion. There's no ten commandments for humans to follow to get into the AI's good books. Even if there was, digital copies of minds and a complete control over matter are much closer to the Hindu and Buddhist ideas of reincarnation than to the various Christian heaven/hell/purgatory combinations.
Even just upvotes and downvotes get me "karma", after all.
[0] I was raised Catholic to get me into a Catholic school, but that's not directly why I read it. My mum thought I wasn't reading enough, so paid me more pocket money for reading more books, and it just happened to be available.
[1] Christ/Yahweh and 12,000 from each of the 12 tribes of Israel, the latter of which makes a lot more sense when considering that the thing was at that point still an offshoot of Judaism, and had not yet developed a long-running antisemitic streak