What did Satan get out of deceiving Eve and Adam into sinning?
Answer : Satan thinks, he got even with God, and had shown to the rest of the fallen angels, how smart and superior he is over men, created in the image and likeness of God.
When Lucifer was cast out from the Heavenly Realm, and lost the anointing and his role as "bearer of light", he lost divine life. No more light, means no more life for Lucifer and the fallen angels.
On the other hand, Adam was cloth with the "light of God" after God anointed him as "High Priest of Humanity", and Adm received the fullness of the gifts, like a Bishop who received the fullness of the priesthood, to impart blessings and graces, and impart the original holiness and justice to the rest of mankind.
https://www.catholicnewsagency.com/resource/55702/adam-high-priest-of-humanity
Lucifer, losing the role of "bearer of light", now had chosen, a new role, an adversarial role.
Satan,[a] also known as the Devil,[b] and sometimes also called Lucifer in Christianity, is an entity in the Abrahamic religions that seduces humans into sin or falsehood. In Judaism, Satan is seen as an agent subservient to Yahweh, typically regarded as a metaphor for the yetzer hara, or "evil inclination." In Christianity and Islam, he is usually seen as a fallen angel or jinn who has rebelled against God, who nevertheless allows him temporary power over the fallen world and a host of demons. In the Quran, Shaitan, also known as Iblis, is an entity made of fire who was cast out of Heaven because he refused to bow before the newly-created Adam and incites humans to sin by infecting their minds with waswās ("evil suggestions").
https://en.wikipedia.org/wiki/Satan
To understand why Satan went first to deceive Eve instead of going directly to Adam to tempt him, we must see the "Authority of Adam" overall creatures, as he named all of them including the cunning serpent, while Eve not yet existed. Plus, Satan only have a "false light" this time, he cannot appear to Adam, in his fallen state, Satan;s false light is inferior to Adam, who was cloth with the light of God. So, tempting Adam indwelling a snake, would easily be rebuked by Adam.
And so, why Eve?
Satan is a cherub, and cherub knows the secrets of God, as God revealed His divine plan to the Angelic Host, to incarnate the Logos thru a chosen Woman.
St.Gabriel was sent by God to announce the "Good News", while Satan came by himself, to announce a "Fake News".
Satan greeted Eve in the garden, while Eve was looking at the Tree of Knowledge of Good and Evil, a symbolic representation of Eve's sacred womb that has roots.
Satan greeted Eve and announced a fake news, and said, Hail Eve, you were chosen to bear the Wisdom of God, you were highly favored. Eve was flattered, why me? In fact, there is only me here in the garden, how can i be chosen? "Is this a prank"?
But ofcourse, Eve was delighted, hearing the fake news, it gives her pride. But, the question was, how can she bear the Wisdom of God? She was not allow to "touch" her sacred womb, which perhaps, has a sacred marking or clothing of protection to remind Adam that God forbidden him, to touch it, a sign of sanctity.
Satan wanted to defile, the sacred womb of Eve, and so, Satan deceive Eve, that he can "touch" it first and will not die.
When Eve saw, that the serpent did not die after touching her sacred womb, she thought, nothing would happen to her too, but the malice of Satan already infected her.
Valtorta Poem has a very detailed description of this event, but Valtorta writings is a forbidden book in Catholic Church.
St.Hildegard writings or poems was approved by the Church, and so it is safe to cite his poem that revealed, how Satan deceived Eve.
"She destroyed her womb by her ignorance."-St.Hildergard
And to show proof, that the Tree of Knowledge of Good and Evil was a symbol for a sacred or virgin womb, we must look at at the Church Father's teachings pointing to Mary as the Tree of Life.
What is the Biblical basis for Mary being the Tree of Life?
If Mary is the Tree of Life, who is her fruit?
"Blessed is the fruit of thy womb, Jesus...." Hail Mary prayer
If Eve, represents the Tree of Good and Evil, then, who was her fruit? Eve fruit was Cain, a murderer like Satan the Father of lies and a murderer from the beginning.
Satan the Devil, had "touch" or defiled Eve's sacred virginity, and Eve bore an offspring coming from Adam tainted by malice of Satan, his name is Cain, a murderer too.
The Children of the Devil
…43Why do you not understand what I am saying? It is because you are unable to accept My message. 44You belong to your father, the devil, and you want to carry out his desires. He was a murderer from the beginning, refusing to uphold the truth, because there is no truth in him. When he lies, he speaks his native language, because he is a liar and the father of lies. 45But because I speak the truth, you do not believe Me!…