The issue has been the notifications getting received with alert type "None", checked by connecting the device to the console logs.
By default, the alert type is expected to be "alert" and hence not setting one should result in an alert type notification. It behaves so, but the filtering works only when the alert type is explicitly set.
So to answer the question, the entitlement is added for the account, and the second app does not need to request for the entitlement again.
Topic:
Code Signing
SubTopic:
Entitlements
Tags: