UberQueue.cs

class UberQueue<T>
{
    private IAsyncQueue<T>[] _queues;
    private Task<T>[] _tasks;

    public UberQueue(IAsyncQueue<T>[] queues)
    {
        _queues = queues;
    }

    async Task<T> DequeueAsync()
    {
        _tasks ??= _queues
            .Select(x => x.DequeueAsync())
            .ToArray();

        await Task.WhenAny(_tasks);

        for (var i = 0; i < _tasks.Length; i++)
        {
            if (_tasks[i].IsCompleted)
            {
                var result = _tasks[i].Result;

                _tasks[i] = _queues[i].DequeueAsync();

                return result;
            }
        }

        throw new InvalidOperationException("No tasks are completed");
    }
}

interface IAsyncQueue<T>
{
    Task<T> DequeueAsync();
}