Does anyone know of any backup utilities for OS/2 which restore an OS/2 installation from a network?
It's not the task of "backup utilities" to restore an installation from a network. A full network-enabled backup/restore solution can do this work. But you're not writing about the target. Restoring to local drives can be done by any bare metal recovery solution. For smaller environments without TSM also SRVIFS can be used.
I'm thinking of something like Clonezilla...
Clonezilla is an program for imaging partitions, that's different from backup/restore. It doesn't run from inside the OS.