From the perspective of Office, there is related Group Policy settings to restrict the permission from seeing the update notification.
Navigate to Computer Configuration>Administrative Templates>Microsoft Office 2016 (Machine)>Updates, then disable the policy Enable Automatic Updates and enable the policy setting Hide Update Notifications.
Based on your description, I think you may get some help from Group Policy team.
You may create a specific group (only including end users or administrators) to apply specific Group Policy settings to group members.
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