Sorry, just looked back and seen that you have:
"He seems simply to be talking about statements of fact: every scientific statement of fact is inevitably about describing the way the world works, as opposed to addressing more existential questions, such as why there’s a world in the first place, which Lewis thinks is religion’s domain."
To a degree I agree, but to my reading he is denigrating science to do that, by reducing it to mere observations, and ignoring the predictive power of science which has, ultimately, led to all the technology that we nowadays take for advantage.
The problem Lewis has is that religion, at the end of the day, is just people spouting their unsupported opinions as though they are facts. The very fact that there are so many religions tells us that most theists have it largely wrong. There is no convincing evidence that Hinduism, for example, is true, while there is that relativity is true.
I fully accept that science cannot answer some of the big questions - but neither can religion! Not in a way that persuades the unconvinced. And Lewis in this quote is trying to promote religion, so he is obliged to play down the huge success of science to make his own religion appear less pathetic.
So while I kind of agree with your position, I will continue to believe Lewis that Lewis was denigrating science in that statement.
And further, I strongly suspect stiggy wiggy particularly likes that quote about science specifically because he is denigrating science, but doing so so subtly most people do not see it.