StartupWithFactorySnippet.cs

public void Configure(IApplicationBuilder app, IWebHostEnvironment env)
{
    // other registrations elided for focus
    app.UseMiddleware<LogUserAgentMiddleware>();
    // the next middleware after ours
    app.UseEndpoints(endpoints =>
    {
        endpoints.MapControllers();
    });
}

public void ConfigureServices(IServiceCollection services)
{    
    services.AddLogging();
    services.AddScoped<LogUserAgentMiddleware>();
    // other registrations elided for focus    
}