@sg1371 I (a persistent overpacker) ended up bringing a carry-on size suitcase (for clothes and stuff for me), a big diaper bag (with stuff for baby and nipple balm), maybe another bag/backpack for phone chargers, fan that I never used, extension cord that I did use, and other odds and ends, and a pillow.
I think the diaper bag (purchased second hand) was the only thing I actually purchased for that purpose, but knew I'd be using it later too. You'll also need to bring your car seat (can leave in the car until ready) - which you probably already knew, but figured I'd mention it. You'll also want to pack an extra empty* bag or two because you're not going to pack things as neatly for the ride home and you'll probably pick up some new items (hygiene items from the hospital room and/or gifts for baby if people are visiting)
But that's me (p.s. I didn't use about half the things I brought/stayed in a hospital gown until discharged, but that pillow that you think is taking up too much space is worth it)
*edit: typo