How to correctly set up DI?

Question

.NET

I'm developing a class structure for my project and I've run into a problem.
I have a WebHelper class, which is essentially a layer between HttpClient and my various services. As a dependency, it takes the HttpClientFactory factory, which, in turn, can return the clients I need. This is done with the intent that both an empty HttpClient and one containing an AuthorizationToken or other Headers may be required. Thus, there is a service that communicates with a third-party data source and needs a token, and there are also a couple of services that do not require anything.
Schematically, all this can be depicted as follows:

ApplicationSolution
  Application.Site
    Startup (регистрация объектов происходит здесь)
  Application.Core
    WebHelper
    HttpClientFactory
  Application.Service1 (требующий Headers в HttpClient)
  Application.Service2 (использует чистый HttpClient)

Since the application uses DI, I pass all the dependencies through the container built into Net.Core. And that's where the problem lies with him. I can register one WebHelper, but for it I need two factories, which must be substituted in the case for Service1 and Service2 are different.
Registration in Startup:

public void ConfigureServices(IServiceCollection services)
{
    services.AddService1(Configuration);
    services.AddService2(Configuration);
    services.AddMvc();
}

Registration in Service1:

public static IServiceCollection AddSerivce1(this IServiceCollection services, IConfigurationRoot configuration)
{
    services.AddSingleton<IHttpClientFactory, HttpClientFactory>(service =>
    {
        var factory = new HttpClientFactory
        {
            Method = () =>
            {
                var jsonType = new MediaTypeWithQualityHeaderValue("application/json");
                var authorizationHeader = new AuthenticationHeaderValue("Basic", token);

                var httpClient = new HttpClient();
                httpClient.DefaultRequestHeaders.Accept.Add(jsonType);
                httpClient.DefaultRequestHeaders.Authorization = authorizationHeader;

                return httpClient;
            }
        };

        return factory;
    });

    services.AddSingleton<IWebHelper, WebHelper>();
    ...            

    return services;
}

Registration in Service2:

public static IServiceCollection AddService2(this IServiceCollection services, IConfigurationRoot configuration)
{
    services.AddSingleton<IHttpClientFactory, HttpClientFactory>(
        service => new HttpClientFactory {Method = () => new HttpClient()});

    services.AddSingleton<IWebHelper, WebHelper>();
    ...

    return services;
}

But with such a record, it turns out that only the second implementation without a token remains alive.
The essence of my question is how to do it correctly. that in one case I will receive a version with a token, and vice versa in another?

Answer 1

Everything is described in "Mark Siman - Dependency Injection in .NET". And including what is DI and the use of containers.