It seems that the old extension was not properly removed when you enabled the new experience. Even though the App Service doesn't show the "Microsoft.ApplicationInsights.AzureWebSites" extension as being installed, the extension is still there and periodically writes ApplicationInsightsProfiler2.
To solve the problem open Kudu and remove this entire folder: "D:\home\SiteExtensions\Microsoft.ApplicationInsights.AzureWebSites".
You might get an access denied (some of the files might be loaded in the running process). If that happens you have 2 options:
- Stop the App Service and try removing the folder again.
- Only remove "D:\home\SiteExtensions\Microsoft.ApplicationInsights.AzureWebSites\applicationHost.xdt" & "D:\home\SiteExtensions\Microsoft.ApplicationInsights.AzureWebSites\scmApplicationHost.xdt" and then restart the AppService. Now the extension is not used anymore and you can safely remove the entire folder.