I am not sure if there is any alert service for watching cost for specific resource but I use the alert for my subscription.
I get alerts when my subscription crosses defined amount say - 50$, 100$, 150$.
It is possible Budget can be set up and then alerts on when budget is crossed
Update:
To set RG scoped budge alert - https://learn.microsoft.com/en-us/azure/cost-management-billing/costs/tutorial-acm-create-budgets#trigger-an-action-group
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