NIOSSH itself doesn't include Mosh support, so adding it would require a mosh client. i didn't include it in the initial beta, because mosh isn't direct fit for tmux control mode, which requires an ordered raw byte stream. i'm planning to add mosh for standalone terminal sessions tho.
thanks for giving it a try. it isn't limited to local networks. Remux connects directly over ssh to any machine reachable from the iPhone, including thru a private network such as tailscale.