Oh congratulations on your first baby, how exciting! I remember when I was packing for my first, I kept second-guessing myself and repacking the bag at least three times the night before, so I totally understand the anxiety you're feeling right now.
For SGH specifically, they do provide the hospital gown during your stay, so you mainly need to bring a comfortable set of clothes and nursing-friendly top for yourself on discharge day, plus one complete outfit for baby to go home in. Someone in my mum group mentioned that SGH gives out a baby bag with some curated items for mum and baby, so that's a nice little bonus you can look forward to. For the recovery essentials, do not skip the donut seat, perineal ice packs, and perineal spray, those are genuinely lifesavers in the first day or two after delivery, and tuck in some Tucks medicated wipes as well. Beyond that, the usual toiletries, phone charger, a swaddle, and a small pack of newborn diapers will cover most of your needs.
Wishing you a smooth and safe delivery, you've got this, mama!