Proxmox storage looks in places defined in /etc/pve/storage.cfg. Usually, not always, this is a directory mounted on the host. For example:
Creating a disk by default labels it by VM ID and by disk ID. So you might have
I tend to copy over this file with the image I wish to restore, with a cp command on the host. If the format of the disk image is different, remember to convert it.
qemu-img convert is great for this purpose.
Proxmox API gives you access to get and set the storage configuration of a VM. Allows for automation or use of different file names.
Also an option is to rebuild. Create new VMs on new disks, install the OS and applications, and restore or recreate data in the guest. With a good business continuity plan, this should be possible, even if it is slower than restoring entire VM images.