The machine images are public so that anyone can use those to bootstrap the their own installation but once created, each individual instance is run within the user’s AWS account and all the resources created are private to that AWS account.
The Galaxy datasets are stored on a persistent EBS volume, which is automatically provisioned and configured if you choose that option at instance launch time (https://launch.usegalaxy.org/catalog/appliance/genomics-virtual-lab → 2. tab → Advanced GVL options → Persistent Volume Storage).
You can attach additional EBS volumes if you’d like but configuring Galaxy to use those is not recommended as it would break the automation methods in place.