There is only 1 permission to allow users to see the Subscriptions list on their profile:
Administer user subscriptions.
But this allows them to see this tab on all accounts. Without this permission set there is no Subscriptions tab for anyone and there is no permission to allow a user to see (only) their Subscriptions tab. Possibly more than 1 bug here or possibly message_subscribe_ui is a work in progress?
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