I’ve given birth in both the US and the UK amd exclusively breastfed both to past a year (with complementary solids at about 6 months). My US baby was born before Obamacare, so there are some changes now (like insurance generally covers pumps, which it didn't before). Generally speaking in the US, the federal government covers women for 12 weeks unpaid time off with job protection. States have their own rules. My state had one of the most generous coverages with up to 14 weeks with partial payment, depending on the circumstances of the birth. Most states have no mandated paid time off. Many employers have their own maternity coverage as a benefit with partial to full pay depending on the individual employer. Technically, no matter what, your job is only protected for the 12 weeks (thats total in a year, including pre and post partum, mind you).
Yes, babies are added to their parent’s health insurance plans when they are born in private/employer sponsored health insurance. The insurance is more expensive when you add kids though. There are government programs to cover low income mothers and children specifically, including food programs that cover formula.
Pushing for the use of formula vs breastfeeding seems to vary a lot by location and socioeconomics. I’ve known people who came home from the hospital with loads of formula samples given to them in the hospital as the forumula reps hock them. I was in a prodominantly well off, well educated liberal area and never saw formula at the hospital. Most people I knew breastfed as well. Honestly, my experience was largely the same in that regard in the UK. There seems to be a great deal of regional variance. I dont know if formula being pushed by the manufactures in the hospitals has changed with Obamacare.
As for pumping in the US, at least in the state I was in, there were laws that mantae that employers must provide a private place that is not a toilet and adequate time for lactating mothers to pump and store milk.
When I was pregnant with my second in the UK, I was curious about the norms around breastfeeding in the UK and one thing I recall seeing is that partnof what makes up the difference in the statistics between the US and the UK is how the data is reported. The US used a more lenient definition amd essentially reported breatfeeding at all and the UK reported breastfeeding only. I dont have this data offhand, though, so don’t quote me on that.
Sorry, that was long, but hopefully I answered some questions.