Custom logger using a service needs same instance

Question

I wrote a custom logger using the ILoggingBuilder and the ILoggerProvider pattern as describe in the .net documentation

My logger needs a service build in the app, I was able to pass the service using the ServiceProvider but unfortunetly the instance is duplicated (even if the service is declared as a singleton)

Here is a sample of the code :

return Host.CreateDefaultBuilder(args)                
                .ConfigureHostConfiguration(configurationBuilder =>
                {
                    if (args is not null)
                    {
                        _ = configurationBuilder.AddCommandLine(args);
                    }
                })
                .ConfigureAppConfiguration((context, builder) =>
                    builder.SetBasePath(AppContext.BaseDirectory)
                        .AddJsonFile("appsettings.json", optional: true))                

                .ConfigureServices((hostContext, services) =>
                {
                    
                    services.AddServices();
                    serviceProvider = services.BuildServiceProvider();
                }
                )
                .ConfigureLogging((hostContext, loggingFactory) =>
                {

                    loggingFactory
                            .AddConsole()
                            .AddEventLog()                            
                            .AddFile("Logs/worker-{Date}.txt")
                            .AddCustomFormatter(serviceProvider.GetService<IMycustomService>());
                });

I've tried many approches but I was not able to use the same instance in my servicesColletion and in my custom logger

Any hep would be greatly appreciated