What is required for the Islam of an apostate who committed apostasy through denial of the Oneness of God (Tawhid) or the prophethood of Muhammad?

Primary text

The statement regarding accepting the Shahada alone applies to one whose apostasy involved denying the Oneness of God, or denying the Prophethood of Muhammad, or denying both. For one who apostatized through other means, their Islam is not established except through an admission of what they denied. If one affirms the prophethood of Muhammad but denies he was sent to all mankind, their Islam is not established unless they testify that Muhammad is the Messenger of Allah to all creation, or disavow all religions contrary to Islam along with the two testimonies. If someone claims Muhammad was sent after a different messenger, they must affirm this current messenger as the Messenger of Allah, as limiting the testimony might imply adherence to their prior belief.