Hi,
I think there might be some misunderstand of how DCRs work so I will start with short explanation of that. Data collection rules define what is collected only. They do not define from which resources the data should be collected. In order to start collecting data from Azure VM for example you assign data collection rule association. The data collection rule association is assigned for the Azure VM and it contains which data collection rule is used for the associations. So in general someone could delete the data collection rule association but not delete the data collection rule and that will result in the Azure VM not collecting the data anymore. With that said the operation name for deleting data collection rule association is microsoft.insights/dataCollectionRuleAssociations/delete and for deleting data collection rule is Microsoft.Insights/dataCollectionRules/delete. As I see that you use Log Analytics for the alert rule I would use =~ to avoid any case sensitivity issues. In order for the alert to apply to all your subscriptions you need to configure all your subscriptions to send diagnostic logs to Log Analytics workspace.
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