I had my babies in the US. Formula was provided in a little under the baby-bassinet storage area (along with manufacturer coupons). If the baby was in the newborn nursery for observation you could ask not to have the nurses feed the baby formula -- I don't know where the formula came from if it was fed in the nursery. Presumably supplied by formula manufacturers who had some arrangement with the hospital. Such is life in a for profit health system. Breastfeeding advocates complained about what looked like hospital sponsorship of formula and maybe they had a point.
The hospital provided all the women's sanitary supplies, and as many as you could hope or wish for pads, ice packs, stretchy post natal granny knickers to accommodate the giant pads and ice packs as well as hospital gowns, the ones that leave you bare in the back; I never encountered anyone wearing their own nightie or T-shirt from home. The trick was to wear two, one tied in front and one tied in back. There were plenty of changes stored in the bedside locker. The pads were a name brand pad and there was a coupon in the bassinet so you could get money off your next packet when you went home.
They also provided all nappies ('diapers') and wipes (again, with coupons from the manufacturer). They were all stored in the little bassinet in a cupboard under where the baby lay. If you wanted to, you could dress your baby in the little shirts the hospital provided actually because of the number of examinations the babies were subjected to (they liked it if you did this instead of clothes from home that took more time to unsnap and close again) and kept the baby wrapped in the cotton flannel receiving blankets they also provided. I still have the little vests and blankets and the little cotton hats made from what looked like a piece of cut up sock with a knot tied at one end the nurse told me they were all mine to take home if I wished after DD1 was born. It would have cost the hospital more to wash and sterilise the baby clothing items than to get new ones.
All I had to bring was a towel and a pair of socks really, plus clothes and underwear to go home in and clothes to put the baby in when going home, and a bag for all the loot (a few nappies and the wipes, a nasal bulb syringe, blanket, little hosp vests and hats). And of course a car seat. They wouldn't discharge you without a car seat.
I did have to wander to the nurses' station at about 7 am the morning after DD1 was born looking for breakfast. It had been delivered to the birthing suite where I had started labour but I had been moved to regular L & D when I had an epidural and DD1 had needed close monitoring, and then I had been transferred to a room, so the kitchen had lost track of me. The nurses managed to find a breakfast for me and I finally ate at around 9 am.
How exactly would you be sure that your own bottles and nipples were being returned to you after sterilisation in a hospital?