internal class Service1
    {
        private readonly Channel<object> _channel = Channel.CreateUnbounded<object>();
        private readonly TaskCompletionSource _taskCompletionSource = new();

        public Task Completion => _taskCompletionSource.Task;

        public async Task EnqueueDataAsync(object data)
        {
            await _channel.Writer.WriteAsync(data);
        }

        public async void Start(CancellationToken ct)
        {
            try
            {
                while (await _channel.Reader.WaitToReadAsync(ct))
                {
                    var item = await _channel.Reader.ReadAsync(ct);
                    // ....
                }

                _taskCompletionSource.SetResult();
            }
            catch (OperationCanceledException) when (ct.IsCancellationRequested)
            {
                _taskCompletionSource.SetCanceled(ct);
            }
            catch (Exception e)
            {
                _taskCompletionSource.SetException(e);
            }
        }
    }

    internal class Service2 : BackgroundService
    {
        private readonly Channel<object> _channel = Channel.CreateUnbounded<object>();
        private readonly TaskCompletionSource _taskCompletionSource = new();

        public async Task EnqueueDataAsync(object data)
        {
            await _channel.Writer.WriteAsync(data);
        }

        protected override async Task ExecuteAsync(CancellationToken ct)
        {
            while (await _channel.Reader.WaitToReadAsync(ct))
            {
                var item = await _channel.Reader.ReadAsync(ct);
                // ....
            }
        }
    }