The sources I have looked at seem to be a bit dividend on this. Because the alcohol percentage is diluted one more time before it reaches the baby’s blood stream, it seems like it shouldn’t matter at all. But still, there are many that do not recommend it.
Pediatric liver function is very different from that of adults, hence why drug regimes for children aren’t just quantities diluted per body weight compared to results but are often entirely different or very restrictive. The effects of alcohol on the brains of developing human children is not extensively studied for obvious reasons, but animals studies (e.g. in mice and rats) show significant detrimental effects. In other words, even small quantities of alcohol may have outsized effects on children, and as the risks of alcohol consumption have been elevated with increasing studies it has become evident that there is no appropriate threshold for ethyl alcohol for infants and small children.
This is from a reliable breastfeeding site that’s been around for years; the woman who runs it was a research physicist before becoming a certified lactation consultant:
“Current research says that occasional use of alcohol (1-2 drinks) does not appear to be harmful to the nursing baby . Many experts recommend against drinking more than 1-2 drinks per week.”
I recall one new mother (back before all the “don’t drink if pregnant” stuff was common, early 80’s) casully mentioned that taking a shot or two of liqueur a little while before breastfeeding helped the baby sleep. Didn’t exactly knock them out, but made them more mellow. (Enough to make the mother warm but not tipsy). It was partly a joke I think but sounded like it was based on experience or advice from older women. .
Still, like actual alcohol consumption in pregnancy, any excess or too repetitive is probably not good for either mother or baby.