@Markus Bartel, Thanks for posting in Q&A. For the local user account, is it already existing on the device? If not, we can create the local account on these Intune managed devices via PowerShell script.
Here is a PowerShell script I use to create a local admin user account "newadmin" for your reference.
$Password=ConvertTo-SecureString <your password> -AsPlainText -Force New-LocalUser "newadmin" -Password $Password -FullName "New admin"
Add-LocalGroupMember -Group "Administrators" -Member "newadmin"
Save the script as admin.ps1 and deploy it via Intune.
https://learn.microsoft.com/en-us/mem/intune/apps/intune-management-extension
Then the local admin account is created and I can login the devices with this account.
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