client_06.cs

class Client : IDisposable
{
    // called from IDisposable.Dispose
    readonly CancellationTokenSource clientLifetimeTokenSource;

    public TimeSpan Timeout { get; }

    public Client(TimeSpan timeout)
    {
        this.Timeout = timeout;
        this.clientLifetimeTokenSource = new CancellationTokenSource();
    }

    public async Task SendAsync(CancellationToken cancellationToken = default)
    {
        using var cts = CancellationTokenSource.CreateLinkedTokenSource(clientLifetimeTokenSource.Token, cancellationToken);
        cts.CancelAfter(Timeout);

        try
        {
            await SendCoreAsync(cts.Token);
        }
        catch (OperationCanceledException ex) when (ex.CancellationToken == cts.Token)
        {
            if (cancellationToken.IsCancellationRequested)
            {
                // Error reason is argument CancellationToken
                throw new OperationCanceledException(ex.Message, ex, cancellationToken);
            }
            else if (clientLifetimeTokenSource.IsCancellationRequested)
            {
                // Error reason is client's dispose
                throw new OperationCanceledException("Client is disposed.", ex, clientLifetimeTokenSource.Token);
            }
            else
            {
                // Error reason is timeout
                throw new TimeoutException($"The request was canceled due to the configured Timeout of {Timeout.TotalSeconds} seconds elapsing.", ex);
            }
        }
    }

    async Task SendCoreAsync(CancellationToken cancellationToken)
    {
        // nanika...
    }

    public void Dispose()
    {
        clientLifetimeTokenSource.Cancel();
        clientLifetimeTokenSource.Dispose();
    }
}