JAMA study showing that babies born to mothers vaccinated during pregnancy had lower risk of infection than those born to unvaccinated mothers. Particularly pre-Omicron and particularly if boosted:
https://jamanetwork.com/journals/jamainternalmedicine/fullarticle/2793109
There's been previous research showing antibody transfer through cord blood during pregnancy and previous research with other vaccines showing protective transfer to babies from vaccination during pregnancy. In addition, a previous study showed coronavirus vaccination reduced the risk of hospitalization in infants born to mothers vaccinated during pregnancy:
https://www.cdc.gov/mmwr/volumes/71/wr/mm7107e3.htm
There's some confounders in this study. Healthy vaccinee bias can't be ruled out. Vaccinated mothers tended to be older and more educated than unvaccinated mothers. But notably infection risk was lower for boosted mothers and during Delta suggesting some vaccine protection effect independent of other habits.
And while infants were excluded if the mother was vaccinated close to birth, some additional effect from breastfeeding can't be ruled out (most mothers in Norway breastfeed). Antibodies do show up in breast milk.
There may also be a cocooning effect from caretakers being vaccinated that may reduce risk of transmission to infants. Though reduced hospitalization risk indicates there is also a direct protection effect.
Vaccination rates for pregnant women are still quite poor especially for BIPOC women. And while the risk of severe COVID is relatively low for infants it is notably higher than the risk of seasonal influenza, and higher for infants than for older children as the risk for children is a U-shaped curve that increases for the very young. Additionally, coronavirus infection increases the risk of birth complications and preterm birth, and the risk of severe COVID is higher for pregnant women, so pregnant women should get vaccinated.