Error when sending message using a quota project

[SMLVE]

[REQUIRED] Step 2: Describe your environment

We are running our API on Google's cloud run.

• Firebase SDK version: FirebaseAdmin version 3.1.0
• Firebase Product: Messaging
• .NET version: 8.0

[REQUIRED] Step 3: Describe the problem

Steps to reproduce:

We are creating a FirebaseApp and retrieving the FirebaseMessaging instance via this code:

public FirebaseMessaging GetFirebaseMessaging()
{
   var apiKey = _contextService.ApiKey;

   var app = _apps.GetOrAdd(apiKey, key =>
   {
       var projectId = $"{_firebaseSettings.Value.ProjectIdPrefix}{key[..8]}-{key[^12..]}";
       var credential = GoogleCredential.GetApplicationDefault().CreateWithQuotaProject(projectId);

       var options = new AppOptions
       {
           Credential = credential,
           ProjectId = projectId,
           HttpClientFactory = _httpClientFactory
       };

       return FirebaseApp.Create(options, key);
   });

   return FirebaseMessaging.GetMessaging(app);
}

With the value returned by the previous method, we send a message using the following code:

var messageId = await messaging.SendAsync(message, cancellationToken);

but we sometimes get the following error:

System.InvalidOperationException: x-goog-user-project header can only be added through the credential or through the <Product>ClientBuilder.
   at Google.Apis.Http.ConfigurableMessageHandler.CheckValidAfterInterceptors(HttpRequestMessage request)
   at Google.Apis.Http.ConfigurableMessageHandler.SendAsync(HttpRequestMessage request, CancellationToken cancellationToken)
   at System.Net.Http.HttpClient.<SendAsync>g__Core|83_0(HttpRequestMessage request, HttpCompletionOption completionOption, CancellationTokenSource cts, Boolean disposeCts, CancellationTokenSource pendingRequestsCts, CancellationToken originalCancellationToken)
   at FirebaseAdmin.Util.ErrorHandlingHttpClient`1.SendAsync(HttpRequestMessage request, CancellationToken cancellationToken)
   at FirebaseAdmin.Util.ErrorHandlingHttpClient`1.SendAndReadAsync(HttpRequestMessage request, CancellationToken cancellationToken)
   at FirebaseAdmin.Util.ErrorHandlingHttpClient`1.SendAndDeserializeAsync[TResult](HttpRequestMessage request, CancellationToken cancellationToken)
   at FirebaseAdmin.Messaging.FirebaseMessagingClient.SendAsync(Message message, Boolean dryRun, CancellationToken cancellationToken)
   at FirebaseAdmin.Messaging.FirebaseMessaging.SendAsync(Message message, Boolean dryRun, CancellationToken cancellationToken)
   at FirebaseAdmin.Messaging.FirebaseMessaging.SendAsync(Message message, CancellationToken cancellationToken)
   at Campaigns.Data.Clients.PushNotificationClient.SendPushNotificationAsync(SendPushNotification pushNotification, CancellationToken cancellationToken) in /src/campaign/src/Campaigns.Data/Clients/PushNotificationClient.cs:line 33

I may be missing something, but the x-goog-user-project header is added automatically via the SDK.