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Do IQ tests have a resolution that is good enough to notice a difference of 3 points?

I think when measuring a big enough populations they likely would show that small of a shift, though would be interested in the range of it, like is it a smaller group highly effected vs being pretty consistent.

I wonder if they account for the noise of the test itself though in their CIs

Looking at the first study, it's not showing a "shift" at all. It's comparing a group of people who recently had covid to a group of people who haven't had covid. Seems like there's some confounders in there, some of which could correlate to IQ.

The second study uses a test with 13 question. I don't think you can ascertain IQ very accurately with a 13 question test (especially if the same test is given to people with a wide range of ages).

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