Asp .Net Core WebApi : 2nd http call on exception – Asp.net

I’m writing one Webapi where I’ve to call a 2nd endpoint of HTTP when the first HTTP endpoint fails. However, for the second HTTP call, my application shouldn’t block the main thread and should return an unsuccessful result. My HTTP client is already equipped with Polly retry policies, and after retries, I want to call the 2nd URL silently without blocking the main thread.
My code looks like below.

public class Request 
{
    public string Id { get; set; }
}

public class Result
{
    public string Id { get; set; }
    public bool IsSuccess { get; set; }       
    public string Message { get; set; }
}

public class Service
{
   private readonly IHttpClientFactory _httpClientFactory;
   private readonly Ilogger _appLogger;
   private readonly string _url1="www.somedomain.com/api1";
   private readonly string _url2="www.somedomain.com/api2";

   Service(IHttpClientFactory factory,Ilogger logger)
   {
     _httpClientFactory = httpClientFactory;
     _appLogger = logger;
   }

   public async Task<Result> Send(Request request)
   { 
        try
        {
         using var client = _httpClientFactory.CreateClient();
         using HttpRequestMessage httpRequest =new HttpRequestMessage(HttpMethod.Post, _url1);
         var req = JsonConvert.SerializeObject<Request>(body);
         var stringContent = new StringContent(req, Encoding.UTF8, "json");
         var result = await client.SendAsync(httpRequest);
         var resultContent = await result.Content.ReadAsStringAsync();
            return JsonConvert.DeserializeObject<Result>(resultContent));
         }
         catch (Exception ex)
         {
            if (ex is OperationCanceledException || ex is TaskCanceledException)
            {
              //Second call needed but don't want to hold the result 
              // Task.Run(async ()=> await Log(request))    //Approach 1 
              // Task.Factory.StartNew(async () => await Log(request)) //Approach 2
              // HostingEnvironment.QueueBackgroundWorkItem(ct => Log(request).ConfigureAwait(false)); //Approach 3
              // QueuedHostedService defined here [Microsoft][1]
              // var jobId = BackgroundJob.Enqueue(() => Log(request).ConfigureAwait(false)); //Approach 4 by hangfire [Hangfire][2]
              // Custome singleton suggested here // [CustomImplementation][1]
            }

            //No 2nd call needed
            await _appLogger.LogAsync(new ExceptionLog(ex));
            return Result{IsSuccess=false;};
         }
   }
   public async Task Log(Request request)
   {
        try
        {
         using var client = _httpClientFactory.CreateClient();
         using var httpRequest =new HttpRequestMessage(HttpMethod.Post, _url2);
         var req = JsonConvert.SerializeObject<Request>(body);
         var stringContent = new StringContent(req, Encoding.UTF8, "json");
         var result = await client.SendAsync(httpRequest);
         var resultContent = await result.Content.ReadAsStringAsync();
         var result = JsonConvert.DeserializeObject<Result>(resultContent));
          await _appLogger.LogAsync("2nd call successful.",result );

         }
         
         catch (Exception ex)
         {
          
            await _appLogger.LogAsync("2nd call failed",ex);
            
         }
   }
}

I was looking for many solutions but am now confused between them.
[1]: https://learn.microsoft.com/en-us/aspnet/core/fundamentals/host/hosted-services?view=aspnetcore-6.0&tabs=visual-studio
[2]: https://www.hangfire.io/
[3]: https://anduin.aiursoft.com/post/2020/10/14/fire-and-forget-in-aspnet-core-with-dependency-alive