Love em or hate em, the Popes quite often write some really thoughtful stuff that stands the test of time (e.g. they have threaded the needle on capitalism vs communism for more than a century).
Catholic church in some sense is massive international company that only promotes internally. So at top you most likely end up with quite similar people who end up as executives in private companies.
(1) Some kind of embodiment, either direct or by proxy, a way to interact with the universe directly and perceive directly.
(2) Recursion and mutability, the capacity to deeply self-modify. (We do this because neurons are literally alive. We're more of a nested Russian doll of sentience I think.)
(3) Being tied metabolically to the thermodynamic arrow of time. You could argue AI already has this, but I'm not sure if it's a direct enough coupling.
Current LLMs lack at least the first two, and probably the third.
I also wonder about a quantum mechanical basis to consciousness. While it's impossible for the brain to be doing discrete qubit style quantum computation (too hot and noisy), it could be doing some other kind of quantum computation, something quite a bit more analogue and stochastic.
If that's true, it may also require quantum computing.
A young man sittin' at a desk with a wooden chair
In what appears to be a high school class
He can see a battlefield, there's giants everywhere
Sayin' the Bible is a thing of the past
In this new age you believe what you wanna believe
'Cause God is whatever you want it to be
And I can hear Mrs. Keen [Sunday school teacher from verse 1] gently say
The God of the past is still God today
Very few who can get the global media to report what they say (and even Popes can only do it intermittently) both have the ability and the desire to use it.