After investigation, the issue comes from the destructor in libraries/SocketWrapper/SocketWrapper.h:

~ZephyrSocketWrapper() {
    if (sock_fd != -1) {
         ::close(sock_fd);
    }
}

Removing these lines prevents the socket from being closed unexpectedly, and the Telnet session works as expected.
I’ve opened the PR with this change, but this is likely not the correct long-term fix.

Tagging @andreagilardoni to see if he can help point us toward the right approach.