Just to conclude, there is no way to use Net::OpenSSH with only one session?

You are not doing anything fanciful, the basic stuff just doesn't seem to work. I can not imagine how you could avoid that issue.

What I don't like in Net::SSH::Any::Backend::Ssh_Cmd it that is going to open a new connection for each command. Right?

Not exactly. Ssh_Cmd runs a new connection for every session. Usually, when the remote side is some server running some Unix/Linux, you run a command per session but in the case of network equipment frequently they provide some custom shell that requires running a conversation against it and executing all commands in the same session. The fact that you want to use Net::Telnet hints in that direction.