HttpClient properties not being passed with DI

I'm working on an ASP.NET Core 5.0 project which has a service that accesses an API. Based on the code below, I'd expect the HttpClient supplied to ToornamentService's constructor to contain the declared BaseAddress and API key header.

However, when debugging, I noticed that the HttpClient never has either of those. BaseAdress is null, and the header is missing. I've tried using an IHttpClientFactory instead of the typed client, but I end up with the same result.

What am I doing wrong?

ConfigureServices Method:

public void ConfigureServices(IServiceCollection services)
    {
        //Omitted for brevity
        services.AddHttpClient<ToornamentService>(c =>
        {
            c.BaseAddress = new Uri("https://api.toornament.com/");
            c.DefaultRequestHeaders.Add("X-Api-Key", Configuration["Toornament:ApiKey"]);
        });

        services.AddTransient<ToornamentService>();
    }

ToornamentService class:

public ToornamentService(HttpClient client)
    {
        Client = client; // client.BaseAddress here is null
    }