HttpClient.Timeout configured by AddHttpClient is ignored

When using the recommended AddHttpClient extension to configure the IHttpClientFactory and include some default HttpClient setup, the value I set for the Timeout property is not seen in the HttpClient instances that I subsequently create.

Demo uses Azure Function, which is like ASP.NET Core.

public class Startup : FunctionsStartup
{
    public static readonly int PushTimeoutMs = 3000;

    public override void Configure(IFunctionsHostBuilder builder)
    {
        builder.Services.AddHttpClient("PushNotification", client =>
        {
            client.Timeout = TimeSpan.FromMilliseconds(PushTimeoutMs);
        });
    }
}

Creating the client.

public class TestFunctionTwo
{
    public TestFunctionTwo(IHttpClientFactory httpClientFactory)
    {
        this.HttpClientFactory = httpClientFactory;
    }

    //

    public IHttpClientFactory HttpClientFactory { get; }

    //

    [FunctionName("TestFunctionTwo")]
    public async Task<IActionResult> Run(
        [HttpTrigger(AuthorizationLevel.Anonymous, "get", "post", Route = null)] HttpRequest req,
        ILogger log)
    {
        await Task.Delay(100);

        return new OkObjectResult($"OK - Timeout: {this.HttpClientFactory.CreateClient().Timeout.TotalMilliseconds}");
    }
}

Returns

OK - Timeout: 100000

This is because you need to create an HttpClient of the same name as the one you've configured, i.e. "PushNotification".

return new OkObjectResult($"OK - Timeout: {this.HttpClientFactory.CreateClient("PushNotification").Timeout.TotalMilliseconds}");