Is Judas liable for his betrayal sin?
Is betrayal a sin, a mortal sin? Yes and No, it depends on whom you betrayed, as Jesus qualifies what kind of betrayal must be condemn.
In Matthew 26:23–25, Jesus confirms the identity of the traitor: "The Son of Man goes, even as it is written of him, but woe to that man through whom the Son of Man is betrayed!
Is Judas, the traitor that Jesus was referring to? The answer is NO!
Did Judas betrayed his friendship with Jesus? Yes. Did Satan entered because of this? NO!
Did Judas betrayed Jesus as "Rabbi"? Yes. Did Satan entered because of this? NO!
Did Judas betrayed Jesus as the "Son of Man"? NO!, Judas never look upon Jesus as the Messiah nor the Son of Man. Judas only look upon Jesus as his friend and Rabbi.
So, what was the sin committed by Judas, that gave Satan the access to enter his soul? In Catholicism it's called sacrilege, and St.Paul described the sacrilege in his letter to Corinthians.
Question:
Is it a more serious sin to receive Communion unworthily than to commit the unconfessed mortal sin?
Answer:
To receive communion unworthily is a form of sacrilege. It would be committing another grievous sin in addition to the mortal sin.
The Catechism of the Catholic Church:
To respond to this invitation we must prepare ourselves for so great and so holy a moment. St. Paul urges us to examine our conscience: “Whoever, therefore, eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty of profaning the body and blood of the Lord. Let a man examine himself, and so eat of the bread and drink of the cup. For any one who eats and drinks without discerning the body eats and drinks judgment upon himself.” Anyone conscious of a grave sin must receive the sacrament of reconciliation before coming to Communion (1385).
This is the sin of Judas, that gave Satan the access to his soul. The mystery question is, why did Jesus gave the holy eucharist or the consecrated bread and wine despite knowing Judas lack of faith in Him as the "Son of Man"?
We can see clearly, that Judas was not the traitor that Jesus was referring to in Matthew26:23-25, because Judas did not betray Jesus as the "Son of Man" but Judas only betrayed his friendship and Jesus as Rabbi.
Back to OP question, "Is Judas liable for his betrayal sin?
Betraying friendship and betraying a Rabbi is a sin against charity, is it a mortal sin? Perhaps No, nor we can judge it as mortal sin.
The clear sin of Judas was described by St.John, he was stealing money, and it is a mortal sin against Ten Commandments, only if the three elements where satisfied by Judas. Did Judas committed the stealing with "full knowledge and full consent"? Maybe yes, maybe no, we cannot judge him.
Did Judas have free will in this matter? Definitely, Judas acted on his freewill when it comes to stealing money and selling Jesus to the High Priest.
Did Judas have freewill in committing the sacrilege, in receiving the dipped bread as the true body,blood, soul and divinity of Jesus Christ? Yes, he committed a sacrilege, but Judas lacks faith in Jesus as the Messiah or the Son of Man, and in this area, Judas can seek forgiveness once his eyes is open to the Truth, that Jesus is indeed the Messiah and the Son of Man.
We can see the reality of Judas asking for forgiveness, when he repented of his sins of betrayal, returning the thirty pieces of silver. Also, since Jesus was the one who gave Judas the eucharist that made him fall into the sin of sacrilege, Jesus has an obligation to save Judas in hell or Hades.
Judas was cast into hell because of the sin of sacrilege aside from stealing money, but remember, Judas is a friend of Jesus, and Jesus lay down His life for all His friends. Jesus has a saving plan for Judas, that's why He allowed Judas to received the holy eucharist.
Judas descended into hell, and when Judas saw Jesus in His Messianic form, preaching the gospel of salvation in Hades, offering the infinite mercy of God, Judas eyes were open, he now clearly see, that Jesus is not only a Rabbi but the prophesied Messiah the Son of Man. And so, Judas, since he had shown repentance, acknowledge his sins before Jesus in hell, and perhaps resemble the words of doubting Thomas saying...
...Jesus my friend, my Rabbi, you are indeed My Lord and My God, my Messiah and the "Son of Man", please forgive me in receiving the dipped bread sacrilegiously...
Will Jesus deny Judas of God's mercy?
Nope! Judas in hell/Hades has now come to knowledge of Truth about who Jesus is, and this is the desire of the Abba Father, for all sinners, to come to knowledge of Christ, and Judas had arrived on that stage..
This is good and pleasing in the sight of God our Savior, 4who wants everyone to be saved and to come to the knowledge of the truth.- 1Timothy2:3-4
The encounter of Jesus and Judas in hell is pleasing to God, because Judas lack of faith were healed, Judas in hell had seen the Truth just like the rest of the souls imprison in Hades, who had not heard or seen Jesus the prophesied Messiah.
So then, did Judas sin or was it Satan inside him sinning?
In terms of betraying Jesus as his friend and Rabbi and stealing money, Judas acted on his freewill and he cannot blame Satan for this fault. While in the sin of sacrilege, Judas had acted irreverently because his mind and heart were already pre-occupied with his planned betrayal, this is also his freewill and cannot be blame on Satan.
Judas acting irreverently in receiving the body,blood, soul and divinity of Jesus Christ is part of his freewill, that gave access to Satan. But since, Judas "lacks faith", his repentance while still alive, and his acknowledgement of Jesus as Messiah the Son of Man, merited salvation, just like the rest of souls in Hades, like Judas, has now come to the full knowledge of who Jesus is, their eyes were open and had seen the Truth.
CCC 633 Scripture calls the abode of the dead, to which the dead Christ went down, “hell” – Sheol in Hebrew or Hades in Greek – because those who are there are deprived of the vision of God.13 Such is the case for all the dead, whether evil or righteous, while they await the Redeemer: which does not mean that their lot is identical, as Jesus shows through the parable of the poor man Lazarus who was received into “Abraham’s bosom”:14 “It is precisely these holy souls, who awaited their Savior in Abraham’s bosom, whom Christ the Lord delivered when he descended into hell.”15 Jesus did not descend into hell to deliver the damned, nor to destroy the hell of damnation, but to free the just who had gone before him.16
Judas and the rest of souls in Hades or hell, whether evil or righteous was given a chance to see Jesus and hear the gospel of Christ. The souls who accepted Jesus offered mercy, was saved but they still have to undergo purging, like Judas and Dimas the repentant thief. While the evil souls, who still rejected the gospel of Christ and do not believe that Jesus is the prophesied Messiah, Jesus had open the "gate of real hell" the hell of damnation, the place for the damned souls, joining the demons.
In closing, Judas had committed the sins of betrayal and stealing money, and the grievous sin of sacrilege that gave Satan accessed to his soul. The sin of sacrilege cast him into hell or Hades, but he was not yet a damned soul nor were cast out in the hell of damnation. Judas escape the hell of damnation, when he accepted the mercy of God that Jesus offered in hell. That's why in Catholic Church, it is a heresy to say that Judas is in hell.
VATICAN OFFICIAL: IT’S HERESY TO SAY JUDAS IS IN HELL
https://www.churchmilitant.com/news/article/vatican-official-claims-its-heresy-to-say-judas-in-hell