Both of these are correct. You can view a full list of Batch feature/service retirements here. Details about the Azure Batch feature pools without public IP addresses (classic) retirement can be found on this page. Since you are not seeing the notice on the service health page it is possible that you do not have any affected pools. Does the email include the impacted resources?
If you are unsure if any of your resources are impacted, I recommend opening a support request. If you don't have a support plan, please let me know and I can enable your subscription for one-time free technical support.
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