There's a couple thing to keep in mind that might help it make sense. Meta-analyses, though not without merit, don't always accomplish the intended goals for a few reasons, two of which this study specifically suffers from. The first is that they combine studies that when they were conducted may have looked at the desired treatments and controls, but they often are doing so in different populations (note they stratify results by elderly, cancer patients etc.) I'm not going to on my phone start pulling the references, but I would venture to guess that the included studies have all sorts of specific groups they were targeting which leads to heterogeniety both in effect size but in interpretation of effect size. Think about it this way, if you are using Dat from many studies with different (often very specific) target populations, does it really make sense to combine them to draw conclusions about a some hypothetical population comprised of those people?

The second thing is sample size. A few thousand seems like a lot until you realize the data in question is incidence. Each subject included either had the disease or they didn't (it's 0 or 1) nothing in-between and nothing outside. Interval inference for dichotomous data (especially when it gets substratified down like the authors have done here) often lead to results like the plain language summary presented. That is, everything is null because they tried to say too much, with too little data.

Takeaway is don't read too much into the findings. The authors were certainly trying to earnestly answer the question (probably), but the existing literature and available data came up short.