Hi @AxelC , welcome to Microsoft Q&A forum.
Could you please try below script by replacing the placeholders with the correct values
Connect-AzAccount
Set-AzContext -Subscription "<your subscription name>"
$storageAccountName ="<your storage account name>"
$resourceGroup = "<your resource group name>"
$storageAccount=Get-AzStorageAccount -ResourceGroupName $resourceGroup -Name $storageAccountName
$ctx = $storageAccount.Context
$tableName = "TableName"
$cloudTable = (Get-AzStorageTable –Name $tableName –Context $ctx).CloudTable
Add-AzTableRow -table $cloudTable -partitionKey "PK2" -rowKey ("CA") -property @{"username"="Chris";"userid"=1}
Reference Article: Add-AzTableRow
Please let us know if this helps or else we can discuss further.