Hello @Marco Muratori,
To resolve the issue with moving your API Management Service, it is important to ensure that all diagnostic settings are removed before attempting the move. If you are unable to find any assigned diagnostic settings through the Azure Portal or CLI, it is possible that there are hidden diagnostic settings that are not immediately visible.
One approach to identify any hidden diagnostic settings is to check for any delete locks that may be applied to the resource or resource group. These locks can prevent the cleanup of diagnostic settings, which may lead to the error you are experiencing. You can remove the delete lock if it exists, and then attempt to remove the diagnostic settings again.
If the issue persists, you may need to investigate further by using Azure Resource Manager (ARM) templates or PowerShell scripts to list all diagnostic settings associated with the resource. This can help uncover any settings that are not visible through the standard interfaces.
I hope this helps resolve your issue. Feel free to reach out if you have further concerns.