I second the rechargeable fan suggestion, especially for a summer birth. Also hair bobbles/bands to tie your hair back, if relevant. Things moved fast with my first and I ended up giving birth with my bags still in the car and it was the fan and hair tie that I was desperate for.
A charged up portable battery pack is good too, and I recommend some of your favourite sweets. I never ate during my labours because they were short, but got through a whole pack of fruit pastilles afterwards.
Take a few changes of your preferred comfy pyjamas. I only had one and foolishly took back my beautiful naked daughter to hold immediately after changing, when she didn’t yet have a nappy on. Immediately got weed on! I had several back up nighties which I’d bought as potential birthing clothes but they weren’t what I really wanted.
On the subject of birthing clothes, with my first I gave birth in the dress I arrived in because there was no time. With my second I had a birthing pool birth in a maternity tankini top, so if you’re thinking of a water birth, don’t forget what you might wear for that.
Also, if you’re planning to breast feed, make sure your going home outfit is suitable for feeding. I messed this up on my second and packed a comfy dress with no boob access.