I'm mainly wondering about whether or not I have used the (TAP) async/await pattern correctly. I get a bunch of these errors, "Because this call is not awaited, execution of the current method continues before the call is completed.", however that sounds like exactly what I want. Which is for the server to be able to handle clients independently and asynchronously.

As a side note, I know it's bad for performance to re-initialize the streams in for example HandleConnection, I just kept it that way for brevity's sake.

Client.cs:

using System.IO;
using System.Net;
using System.Net.Sockets;
using System.Threading.Tasks;

class Client {
    TcpClient tcpClient;
    public void Connect() {
        ConnectAsync();
    }

    public async void Ping() {
        await SendMessage("Ping!");
    }

    private async Task ConnectAsync() {
        tcpClient = new TcpClient();
        await tcpClient.ConnectAsync(IPAddress.Parse("127.0.0.1"), 3344);
        MainWindow.ClientLog("Connected to server!");

        HandleConnection(tcpClient);
    }
    
    private async Task HandleConnection(TcpClient tcpClient) {
        NetworkStream ns = tcpClient.GetStream();
        StreamReader sr = new StreamReader(ns);
        string message = await sr.ReadLineAsync();
        MainWindow.ClientLog("Received message from server: " + message);

        HandleConnection(tcpClient);
    }

    private async Task SendMessage(string message) {
        NetworkStream ns = tcpClient.GetStream();
        StreamWriter sw = new StreamWriter(ns);
        await sw.WriteLineAsync(message);
        await sw.FlushAsync();
        MainWindow.ClientLog("Sent Ping! to server.");
    }
}

Server.cs:

using System.Collections.Generic;
using System.IO;
using System.Net;
using System.Net.Sockets;
using System.Threading.Tasks;

class Server {
    List<TcpClient> connectedClients;
    public void Host() {
        connectedClients = new List<TcpClient>();
        HostAsync();
    }

    private async Task HostAsync() {
        IPEndPoint local = new IPEndPoint(IPAddress.Parse("127.0.0.1"), 3344);
        TcpListener mainListener = new TcpListener(local);

        mainListener.Start();
        MainWindow.ServerLog("Server started.");
        while(true) {
            TcpClient client = await mainListener.AcceptTcpClientAsync();
            MainWindow.ServerLog("Client connected!");

            connectedClients.Add(client);
            HandleClient(client);
        }
    }

    private async Task HandleClient(TcpClient client) {
        NetworkStream ns = client.GetStream();
        StreamReader sr = new StreamReader(ns);
        string message = await sr.ReadLineAsync();
        MainWindow.ServerLog("Message from client nr. " + connectedClients.IndexOf(client) + ": " + message);

        if (message == "Ping!") {
            await SendMessage(client, "Pong!");
        }

        HandleClient(client);
    }

    private async Task SendMessage(TcpClient client, string message) {
        NetworkStream ns = client.GetStream();
        StreamWriter sw = new StreamWriter(ns);
        await sw.WriteLineAsync(message);
        await sw.FlushAsync();
        MainWindow.ServerLog("Sent message to client: " + message);
    }

    private async Task SendMessages(IEnumerable<TcpClient> clients, string message) {
        foreach (TcpClient client in clients) {
            SendMessage(client, message);
        }
    }
}