I understand you have some VMs with the tag=PURPOSE. You are wanting to get a list of these VMs and also the value of the PURPOSE tag. Please let me know if I am misunderstanding the issue.
Please try this command and see if it works for you. During my testing it outputted the expected results.
Get-AzResource -ResourceType Microsoft.Compute/virtualMachines -TagName "PURPOSE" | Format-Table Name, @{Name='PURPOSE'; Expression={$_.Tags['PURPOSE']}}
Hope this help! Let me know if you still have questions.
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