How to load assembly path in the new runtime experience in Automation Accounts' runbooks?

Question

We have a runbook that we use to log to Application Insights. We use it for making logs both from Azure and Hybrid workers. In hybrid workers the logging works correctly, but in Azure it fails with

Cannot find type [Microsoft.ApplicationInsights.TelemetryClient]: verify that the assembly containing this type is loaded

Here's how we load the assembly to use the Microsoft.ApplicationInsights module in the code:

$AssemblyPathAzure = "C:\Modules\User\Microsoft.ApplicationInsights\Microsoft.ApplicationInsights.dll"
$AssemblyPathHybridWorker = "C:\Program Files\WindowsPowerShell\Modules\microsoft.applicationinsights.2.20.0\lib\net46\Microsoft.ApplicationInsights.dll"
try {Add-Type -Path $AssemblyPathAzure}
catch  { $_.Exception.LoaderExceptions }

try {Add-Type -Path $AssemblyPathHybridWorker}
catch  { $_.Exception.LoaderExceptions }

I've also tried the following path:

$AssemblyPathAzure = "C:\Modules\Global\Azure\Compute\Microsoft.ApplicationInsights.dll"

Both don't work in Azure.

I have a feeling that the import from "C:\Modules\User\Microsoft.ApplicationInsights\Microsoft.ApplicationInsights.dll" used to work before Accounts migrated to the new Runtime Experience

Could you help out with this issue?