Azure.RequestFailedException: 'The principal `***` lacks the required data action

I'm trying to use any of C# samples that leverage using PersistentAgentsClient.
I guess, the problem is the configuration, which is not clearly described.

For example, the following code fails:

 PersistentAgentsClient client = AzureAIAgent.CreateAgentsClient("https://***-resource.services.ai.azure.com/api/projects/my-agents-samples", new AzureCliCredential());

 PersistentAgent definition = await client.Administration.CreateAgentAsync(
     "gpt-4o",
     name: "SkAgent01",
     description: "Sample Agent",
     instructions: "Helper");

Getting the following error:

Azure.RequestFailedException: 'The principal *** lacks the required data action Microsoft.CognitiveServices/accounts/AIServices/agents/write to perform POST /api/projects/{projectName}/assistants operation. For instructions on granting the necessary permissions, see https://aka.ms/FoundryPermissions.
Status: 401 (PermissionDenied)

Btw. I have created the project. I'm logged in CLI for sure.

My user is added twice in the user's list: Cognitive Services User and Cognitive Services Contributor.

I have tried using AzureCliCredential and DefaultAzureCredential. Is there some way to use the ApiKey?