Current status: Breastmilk-IQ relationship inconclusive and hotly contested (Breastmilk-health status understood and strongly favorable)
You provided a link to a meta-study from 2013, but 44 articles cite that article many do not agree.
Source?
So the author cites findings that how-long you breastfeed for or amount of breastfeeding you do has an effect (e.g. once a day vs twice a day) that's a big unexplained phenomenon (which could NOT be explained by maternal IQ, SES, etc).
To quote this author's interpretation of the literature "Although the topic is controversial, and a recent systematic review identified heterogeneity between studies, among the 4 studies with the least bias (each >500 subjects, controlled for maternal IQ, breastfeeding recall duration <3 years) breastfeeding improved performance on IQ testing by 1.76 points (95% confidence interval, 0.25–3.26), suggesting a small but durable impact of breastfeeding on intelligence.10"
(Again 2017, fully aware of the difficulty of controlling [1])
Now does this case-closed prove breastmilk bumps IQ? No, it proves my original claim that this is hotly contested.
1. Breastfeeding: What Do We Know, and Where Do We Go From Here?
It could be explained by maternal IQ and SES, e.g. if higher IQ mothers were more likely to stick to optimal breastfeeding practices.
> Now does this case-closed prove breastmilk bumps IQ? No, it proves my original claim that this is hotly contested.
That may well be true, but the fact that the issue is "hotly contested" after decades of research is telling. If the effect was significant (practically, rather than statistically), you'd expect it to be pretty well established after decades of research. Instead, in properly controlled studies and meta-analyses, even where the effect exists, it is small (1.76 IQ points in your example, 2.62 in a study by Horta).