StartupTaskBuilder.cs

public class StartupTaskBuilder
{
    ...
    private class StartupTaskSequencer : IStartupTaskSequencer
    {
        public StartupTaskSequencer(Queue<IStartupTask> tasks) => _tasks = tasks;

        public async Task StartAsync(IStartupTask task)
        {
            foreach (var next in _tasks.SkipWhile(x => x != task))
            {
                if (await next.CanRunAsync())
                {
                    await next.RunAsync();
                }
            }
        }

        public Task StartAsync() => StartAsync(_tasks.FirstOrDefault());

        private readonly Queue<IStartupTask> _tasks;
    }
}