~~Stop. Docker is not a hypervisor and shouldn't be used as one.
Either use a docker compose file to do automated deployments or move to Proxmox and use host templates to deploy VMs which then can host docker.
There is zero reason to run KVM in docker.~~
Never mind, I misread. What you are looking for is Ansible. You can create a VM template that has your SSH keys configured and then you use Ansible to spin up a VM and do stuff instead the VM. I know how to do this under Proxmox but I have no idea how to do it under pure Debian. A lot of it is probably the same.