Is inserting the penis into the anus once considered zina (fornication/adultery) for which the hadd (prescribed punishment) is applied, and does it fall under the warning against fornicators, knowing that the questioner has repented, feels remorse, and fears not being forgiven?

What you did is an abomination and fornication. Fornication is the act of committing indecency in the front or back passage. Repentance is accepted from whoever performs it correctly, and its door is not closed to anyone. Allah Almighty is Forgiving and Merciful. Whoever repents and turns to Him, Allah will accept their repentance. A repentant person returns as if they had no sin, for the Prophet, peace and blessings be upon him, said: "The one who repents from sin is like one who has no sin." And Allah Almighty says: "Say, 'O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allah. Indeed, Allah forgives all sins. Indeed, it is He who is the Forgiving, the Merciful.'" If your repentance is sincere, then rejoice in Allah's forgiveness, and increase your supererogatory acts of worship and good deeds which erase evil deeds. You are not required to go to someone who will inflict the legal punishment upon you. Rather, conceal yourself with Allah's concealment, accept His well-being, and repent between yourself and Him. You must avoid those who commit such abominations, accompany righteous people, and supplicate frequently.