Concurrency in Azure Function fails. BlobTrigger .NET8 C#

Question

I have an Azure Function App with a BlobTrigger function. It triggers when a new blob is stored in the blob storage and uploads it to a DB. It is configured to have dynamic concurrency. When a blob arrives it triggers and uploads it to the DB. But when two or more blobs arrive at the same time, it triggers for all of them, but it only uploads one to the DB. I am using

Microsoft.Azure.Functions.Worker.Extensions.Storage.Blobs Version="6.2.0"

This is my host.json file:

{
  "version": "2.0",
  "logging": {
    "applicationInsights": {
      "samplingSettings": {
        "isEnabled": true,
        "excludedTypes": "Request"
      },
      "enableLiveMetricsFilters": true
    },
    "logLevel": {
      "Host.Concurrency": "Trace"
    }
  },
  "concurrency": {
    "dynamicConcurrencyEnabled": true,
    "snapshotPersistenceEnabled": true
  }
}