If you're in the tub, or water, something to scoop out matter with (whether this be fecal matter, clots, clumps of vernix... doesn't matter!)
Bendy straws!!! I remember hearing someone say it's the only thing in everyone's birth kit that is guaranteed use. ;)
A few chux pads, disposable or washable. Washable large ones you can get away with 1-2, but the disposable ones you've gotta have at LEAST five of.
For me I had some herbal tinctures that were necessary for complications or problems: angelica, shepherd's purse, nettles, hops, yellowdock...
A shower curtain for the bed in case you give birth there.
Fishy pool if you're doing pool birth.
Those fishnet underwear things that hold your pads in place. A godsend!
Some prefolds for you to 'wear' in your underwear or sit on, also to wrap baby's bum in (to catch post birth mec!)
Can't think of anything else I really needed or used, to be honest...
Now, what you may NOT need:
We didn't use "sterilized scissors" (not really as sterile as you think they are if you just boiled them) and floss for the cord, we had a lotus birth so it wasn't necessary. Your normal scissors, washed well will work just as fine and pretty much do the same thing as boiling it, tbh.
Didn't find any use with a peri bottle (just kept a measuring cup in the bathroom instead).
Disposable maxi pads, Depends or hospital lochia pads. Cloth pads, and prefolds, work just fine. :)
Antibiotic gel for baby: Gel is for active Clap infections, to prevent bacteria from getting in baby's eyes, which when left untreated to fester for a while has a small chance of causing bilndness. When you break it down they're more likely to die of a falling coconut than get this, so even if you DO have an active infection I'd read up more to be sure.
Vitamin k? Unless you have a blood clotting disorder, an extremely physically traumatic birth (for baby, involving heavy bruising), cannot breastfed, give birth in a sterile environment or are extremely deficient there's no reason to do this. Plus, there are risks from both the drops and the shot.
Bulb syringe. Traumatic for baby, and doesn't actually help as much as it makes things worse.