Even in domains where (virtually) all the knowledge is available, and most tasks are exact variations of what has come before, like programming, the most powerful AI systems are mediocre, bordering on competent. Outside this idealised case, they may have "infinite patience for our questions" (up to the token limit, anyway), but they largely lack the capacity to provide answers.
Medical research is about the best example you could pick for something that current-gen AI systems cannot do. Most of the information about the human body is located in human bodies, and wholly inaccessible to every AI system. An extremely important part of medical research is identifying when the established consensus is wrong: how is AI to do that?
There is no reason to believe that LLMs will ever meaningfully contribute to medicine, in much the same sense there is no reason to believe that lawn ornaments will. Pen-and-paper calculations, and the engineering / manufacturing / etc work of humans, took us to the moon: the computers acted as batch processors and task schedulers, nothing more. Medical research done by humans is responsible for the past century of medical improvements. As much as I like computers, they won't be people for the foreseeable future.
Death is horrifying, but an unfounded belief that AI will save you is not a healthy coping mechanism. If you're looking for religion, there are far better ones. And if you don't think you're looking for religion, perhaps the "death gives life meaning" philosophies might suffice? All Men are Mortal by Simone de Beauvoir was presumably some comfort to its author, who also wrote:
> There is no such thing as a natural death: nothing that happens to a man is ever natural, since his presence calls the world into question. All men must die: but for every man his death is an accident and, even if he knows it and consents to it, an unjustifiable violation.
(quotation from A Very Easy Death via https://martyhalpern.blogspot.com/2011/04/j-r-r-tolkien-quot...)