LAPS Creation using Intune

I find it weird that the user is not being added to the local admin group.
What I would do is build a troubleshooting mechanism to understand at which point it fails.
First of all if you run the script that creates the user and add it to the local admin group locally on a local machine or on demand on a test machine, does it work?

If yes then add some logging to your script:

Start-Transcript -Path "C:\ProgramData\Microsoft\IntuneManagementExtension\Logs\LocalAdminScriptLogs.txt" -Append -ErrorAction Stop

try{
    # you code goes here with write hosts to depict the code flow into the log file 
    # add -ErrorAction stop to throw errors to the catch clause
}
catch{
    # depict the error to the log file
    Write-Error "An error occurred during detection: $_"
}
finally{
    Stop-Transcript
}

Then you could collect the logs following this guide.