There are a lot of weak studies in many fields, largely pushed by how current funding and work practices in these areas are.
It can be very strange how many very weak studies are then widely promoted as the truth, though a lot of that is the media likes a good firm headline and then people run with it. The amount of news stories on science where if you go to the actual study says nothing of the sort and then it gets lost in transmission the further out, often getting more certain and absolute as they go.
This is kinda standard in a lot of areas, annoying, but not really surprising.
Again that’s a benefit to you not the baby.
Things that benefit the mother can also benefit the baby indirectly, much as things that benefit the baby can also benefit the mother indirectly. They don't need to be in neat categories of one or the other nor do they need to be put into a hierarchy as if thing that benefit the mother are less important.
I didn't get much of the benefits talk when I was pregnant with my first. No antenatal breastfeeding clinics or anything was offered to me. There was some talk about increased risks with formula feeding, but in very vague terms and it was generally believed that as a teen mother that it would be too much on me to breastfeed correctly so it wasn't really discussed. Socially, other than my spouse, I was largely told that I probably wouldn't be able to and if I did I shouldn't do long because it's disgusting. If anything, I probably ran on spite to get me through the sleep deprivation those first few months and gum pearls which they say shouldn't bother a baby, but my oldest disagreed strongly.
Breastfeeding fit into my lifestyle which is a large part of why I could do it for so long. It doesn't fit into many women's lifestyle, we're not in a society built around that or anything else to do with women's bodies and as mixed feeding isn't promoted and many who can breastfeed biologically can't pump, there are a lot of social and biological barriers. Trying to go on about the benefits of breastfeeding doesn't tend to do much good and often ignores the social issues involved and instead just blames women for either not doing enough or for doing too much whichever way a baby gets fed.