They might like you to bring the pushchair in rather than carrying baby but I'm not 100% sure on that. I'd ask them to check the seat in the car rather than buy a separate one just for taking baby home. 😊 Probably a question for your midwife!
We had a prep online class from our hospital QCCH and they told us that for safety reasons the baby needs to leave the hospital in something to be carried in other than your arms. It could be a car seat, a pram or even a moses basket. But I guess every trust is different, I would ask just in case
I’d double check with your hospital. I thought they had to check it when I had my first in 2023 but they said they didn’t do that