Code to reproduce issue with state using azure provider in pulumi..

AppInsightApiKey.cs

using System.Collections.Generic;
using System.Threading.Tasks;

using Pulumi;
using Pulumi.Azure.AppInsights;
using Pulumi.Azure.Core;
using Pulumi.Azure.Storage;

class Program
{
    static Task<int> Main()
    {
        return Deployment.RunAsync(() => {

            // Create an Azure Resource Group
            var resourceGroup = new ResourceGroup("testpulumi");

            var appInsights = new Insights("appInsights", new InsightsArgs
            {
                ApplicationType = "web",
                ResourceGroupName = resourceGroup.Name,    
            });

            var appInsightApiKey = new ApiKey("ai", new ApiKeyArgs
            {
                ApplicationInsightsId = appInsights.Id,
                ReadPermissions = "api"
            });

            // Export the connection string for the storage account
            return new Dictionary<string, object?>
            {
                { "AppInsightKey", appInsightApiKey.Key }
            };
        });
    }
}