By default when you create TestServer it doesn't build configuration and you need to build configuration and pass it to the test server.

public class ContestTest
{
    private readonly HttpClient _httpClient;

    public ContestTest()
    {
        var environment = "Development";
        var directory = Directory.GetCurrentDirectory();
        var configurationBuilder = new ConfigurationBuilder()
            .SetBasePath(directory)
            .AddJsonFile("appsettings.json")
            .AddJsonFile($"appsettings.{environment}.json");

        var server = new TestServer(new WebHostBuilder()
            .UseEnvironment(environment)
            .UseConfiguration(configurationBuilder.Build())
            .UseStartup<Startup>());

        _httpClient = server.CreateClient();
    }
}

Your test project is likely built into a different directory than your main project, so your appsettings.Development.json file is not there.

Load your settings with IConfigurationBuilder in your Startup. You can specify a relative path there through AddJsonFile method.

Also do you really need to start a server in your unit test? You test class functionality, which rarely needs a running server. In order to inject test settings into a class test you could use the options pattern and than in your test provide dummy settings via Options.Create(new MyDummySettings()).