Add cookies to a request using IHttpClientFactory in Blazor

Question

I have a Blazor project which depends on an external API. When I login into my website I make an API call to get a session token, then I store this token into a claim.

This token must be send in any call as a cookie. For this, since I'm trying to use HttpClient, I use Header Propagation as seen here.

So my builder has a service like this:

services.AddHttpClient<ServiceClient>(client =>
{
    client.BaseAddress = new Uri(url);
    client.DefaultRequestHeaders.Accept.Add(new MediaTypeWithQualityHeaderValue("application/json"));
})
.ConfigurePrimaryHttpMessageHandler(() => new HttpClientHandler()
{
    ClientCertificateOptions = ClientCertificateOption.Manual,
    ServerCertificateCustomValidationCallback = (httpRequestMessage, cert, cetChain, policyErrors) => { return true; },
})
.AddHeaderPropagation(options =>
{
    options.Headers.Add("Cookie");
});

services.AddHeaderPropagation(options =>
    options.Headers.Add("Cookie", context =>
    {
        var identity = context.HttpContext.User.Identities.FirstOrDefault(x => x.AuthenticationType == "AppAuthenticationType");
        if (identity?.IsAuthenticated ?? false)
            return $"SESSION={identity.GetSession()}";
        return String.Empty;
    }));

Then I add app.UseHeaderPropagation(); after app.UseAuthentication(); and app.UseAuthorization(); to get it to work.

The problem I have is when I first open my website, I'm not logged in so my claims are not set yet. When I log-in, I set my claims so I can get my session token, but the service is already done so my token is not been at all.

How can I force this header propagation to be resolved for every call?