Once dried and sterilised I’ll transfer to another storage box as I usually accumulate and wash so there won’t be enough space. I personally don’t like to put my items on the top shelf as it yellows the teats, bottles and parts more easily. I use something like this: https://shp.ee/49ixk3m
I will take out those that are already done and store in a ziploc bag. Then continue the next batch.