Is there expiation for the act of sodomy (without penetration), and what is the ruling concerning the one who commits it?

What you did is considered sodomy in a general sense if you were aware of your actions, but it is not the type of sodomy that necessitates a hadd (prescribed punishment).

You must repent, feel remorse, and make a sincere resolve not to return to such an act. Indeed, through sincere repentance, Allah forgives sins. It has been mentioned in the Holy Qur'an: "But indeed, I am the All-Forgiving to whoever repents, believes, and does righteousness, and then is guided." (Taha: 82), and "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."" (Az-Zumar: 53), and "Your Lord has decreed upon Himself mercy: that whoever of you does evil in ignorance and then repents after that and corrects himself – indeed, He is Forgiving and Merciful." (Al-An'am: 54).

And in the Hadith (definition) Qudsi: "O son of Adam, as long as you invoke Me and hope in Me, I will forgive you for what you have done, and I do not care. O son of Adam, were your sins to reach the clouds of the sky and you then ask for My forgiveness, I would forgive you. O son of Adam, were you to come to Me with sins nearly as great as the earth and meet Me without associating anything with Me, I would come to you with forgiveness nearly as great as it." And the Prophet, peace and blessings be upon him, said: "Remorse is repentance."