The implemented solution solves the problem of having to login and logout after having enabled permissions to use the local network.

However, because of a behaviour of macOS, this solution doesn't work any longer after the mac is rebooted. There are two possible workarounds to make the NoMachine client to work again after a reboot:

1) disable and re-enable permissions for the local network 

or 

2) turn off and on the wifi or the LAN.

(ref.  https://kb.nomachine.com/AR09V01251)

The release of MacOS Sequoia introduced new permissions for all applications accessing the LAN.

When the client is launched, the authorization to retrieve devices on the local LAN is requested.

Even if the user clicks on 'Accept', given permissions are ignored by the system and the client is unable to find NoMachine servers in LAN. If the user connects by using the server IP, connection fails with "No route to host". 

Possible workarounds are:

1) try re-logging in (logout-login on local), then connect again via NoMachine.

2) or launch the NoMachine client from a terminal:

/Applications/NoMachine.app/Contents/MacOS/nxplayer