Yes that's it: "cat > /dev/null". Or you can even skip running cat and just "> /dev/null". You exit by typing ctrl-d which sends an EOF (and then sends all the output to /dev/null!).
I am not sure if the noteux.com works in the same way.
I am also not sure but is there a way to create persistant terminal connections as each is going to /dev/null but its persistant and you can connect to any of it?
maybe using zellij / tmux