LazyCache: Regularly refresh cached items

I am using LazyCache and want to have cache refreshed e.g. every hour, but ideally I want the first caller after the cache item expired do not wait for cache reloaded. I wrote the following

public async Task<List<KeyValuePair<string, string>>> GetCarriersAsync()
{

    var options = new MemoryCacheEntryOptions
    {
        AbsoluteExpirationRelativeToNow = new TimeSpan(1,0,0),// consider to config
    }.RegisterPostEvictionCallback(
         async  (key, value, reason, state) =>
        {
            await GetCarriersAsync();//will save to cache
            _logger.LogInformation("Carriers are reloaded: " );
        });
    Func<Task<List<KeyValuePair<string, string>>>> cacheableAsyncFunc = () => GetCarriersFromApi();
    var cachedCarriers = await _cache.GetOrAddAsync($"Carriers", cacheableAsyncFunc, options);

    return cachedCarriers;
}

However RegisterPostEvictionCallback is not called when cache item is expired, but only when the next request to the item occurred (and the caller need to wait for a lengthy operation).

The thread Expiration almost never happens on it's own in the background #248 explains that this is by design, and suggests workaround to specify CancellationTokenSource.CancelAfter(TimeSpan.FromHours(1)) instead of SetAbsoluteExpiration.

Unfortunately LazyCache.GetOrAddAsync doesn’t have CancellationToken as a parameter. What is the best way to trigger reload of cache on a scheduled time with minimal waiting time for the first user?

I found the similar question In-Memory Caching with auto-regeneration on ASP.Net Core that suggested to call the AddExpirationToken(new CancellationChangeToken(new CancellationTokenSource(_options.ReferenceDataRefreshTimeSpan).Token).

I tried it, but didn't make it working. However the same answer had alternative(and recommended) option by using timer. I've created a class RefreshebleCache that I am using for different cachable options like the following:

   var refreshebleCache = new RefreshebleCache<MyCashableObjectType>(_cache, _logger);
   Task<MyCashableObjectType> CacheableAsyncFunc() => GetMyCashableObjectTypeFromApiAsync();
   var cachedResponse = await refreshebleCache.GetOrAddAsync("MyCashableObject", CacheableAsyncFunc,
                        _options.RefreshTimeSpan);

The RefreshebleCache implementation:

/// <summary>
    /// Based on https://stackoverflow.com/questions/44723017/in-memory-caching-with-auto-regeneration-on-asp-net-core
    /// </summary>
    /// <typeparam name="T"></typeparam>
    public class RefreshebleCache<T>
    {

        protected readonly IAppCache _cache;
        private readonly ILogger _logger;
        public bool LoadingBusy = false;
        private string _cacheKey;
        private TimeSpan _refreshTimeSpan;
        private Func<Task<T>> _functionToLoad;
        private Timer _timer;

        public RefreshebleCache(IAppCache cache, ILogger logger)
        {

            _cache = cache;
            _logger = logger;
        }

        public async Task<T>  GetOrAddAsync (string cacheKey , Func<Task<T>> functionToLoad, TimeSpan refreshTimeSpan)
        {
            _refreshTimeSpan= refreshTimeSpan;
            _functionToLoad = functionToLoad;
            _cacheKey = cacheKey;
            var timerCachedKey = "Timer_for_"+cacheKey;
            //if removed from cache, _timer could continue to work, creating redundant calls
            _timer =  _appCache.GetOrAdd(timerCachedKey, () => 
             CreateTimer(refreshTimeSpan), 
  SetMemoryCacheEntryOptions(CacheItemPriority.NeverRemove));
            var cachedValue = await LoadCacheEntryAsync();
            return  cachedValue;
        }
        private Timer CreateTimer(TimeSpan refreshTimeSpan)
        {
            Debug.WriteLine($"calling CreateTimer for {_cacheKey} refreshTimeSpan {refreshTimeSpan}"); //start first time in refreshTimeSpan
            return new Timer(TimerTickAsync, null, refreshTimeSpan, refreshTimeSpan);
        }

    
        private async void TimerTickAsync(object state)
        {
            if (LoadingBusy) return;
            try
            {
                LoadingBusy = true;
                Debug.WriteLine($"calling LoadCacheEntryAsync from TimerTickAsync for {_cacheKey}");
                var loadingTask = LoadCacheEntryAsync(true);
                await loadingTask;
            }
            catch(Exception e)
            {
                _logger.LogWarning($" {nameof(T)} for {_cacheKey} was not reloaded.    {e} ");
            }
            finally
            {
                LoadingBusy = false;
            }
        }
        private async Task<T> LoadCacheEntryAsync(bool update=false)
        {
            var cacheEntryOptions = SetMemoryCacheEntryOptions();

            Func<Task<T>> cacheableAsyncFunc = () => _functionToLoad();
            Debug.WriteLine($"called LoadCacheEntryAsync for {_cacheKey} update:{update}");
            T cachedValues = default(T);
            if (update)
            {
                cachedValues =await cacheableAsyncFunc();
                if (cachedValues != null)
                {
                    _cache.Add(_cacheKey, cachedValues, cacheEntryOptions);
                }

                //    _cache.Add(_cacheKey, cacheableAsyncFunc, cacheEntryOptions);
            }
            else
            {
                 cachedValues = await _cache.GetOrAddAsync(_cacheKey, cacheableAsyncFunc, cacheEntryOptions);
            }
            return cachedValues;
        }
        private MemoryCacheEntryOptions SetMemoryCacheEntryOptions(CacheItemPriority priority= CacheItemPriority.Normal)
       {
          var cacheEntryOptions = new MemoryCacheEntryOptions
          {
            Priority = priority 
          };
          return cacheEntryOptions;
        }

 }

}