Subscribe Powershell Information, Warning and Error stream AddData event - powershell

Question

I'm building a wrapper around PowerShell scripts to handle logging in one unified way. The idea is to intercept messages from information/warning/error streams and log them in chronological order using different sinks (console/file/db etc). For that purpose, I'd like to utilize events that occur when some data is added to a corresponding stream. That's where I'm now:
$ps = [PowerShell]::Create("CurrentRunspace")
$ps.AddScript({
Write-Information 'Information'
Write-Warning 'Warning'
Write-Error 'Error'
exit -1
}) # in reality here should be script that is wrapped
$output = [System.Management.Automation.PSDataCollection[object]]::new()
$ps.Streams.Information.Add_DataAdded({
# $output.Add($_) is for example, in reality, any handler could be added
$ps.Streams.Information.ReadAll().ForEach{ $output.Add($_) }
})
$ps.Streams.Warning.Add_DataAdded({
# $output.Add($_) is for example, in reality, any handler could be added
$ps.Streams.Warning.ReadAll().ForEach{ $output.Add($_) }
})
$ps.Streams.Error.Add_DataAdded({
# $output.Add($_) is for example, in reality, any handler could be added
$ps.Streams.Error.ReadAll().ForEach{ $output.Add($_) }
})
# run script
$results = $ps.Invoke()
$exitCode = $LASTEXITCODE
# these lines are just for the test
Write-Host $exitCode
Write-Host "$([string]::Join(', ', $output))"
Expected content of $output:
-1
Information
Warning
Error
Actual content of $output:
-1
Error
Do you guys know why a subscription to the Warning and Information DataAdded event doesn't work?