Not the person you asked, but we have something similar to what you described - our GitLab is self-hosted on Hetzner cloud and the build machine is a beefy bare metal machine in the same datacenter (plus an additional Mac in our office just for iOS). Built images are stored in GitLab repository and deployed from there.
We deploy to AWS (among others) and had no issues regarding traffic price since it's ingress into AWS.
We deploy to AWS (among others) and had no issues regarding traffic price since it's ingress into AWS.