Yes, I would say that our eternality is an aspect of bearing His image.
It is true that the angels are never said to have been created by the breath of God. But it is also true that they will suffer being cast out from his presence forever - the very verse you cited is a classic proof for that. In fact, I believe they will suffer on a level far worse than humans.
When II Peter 2:4 says that God spared not the angels that sinned, but cast them down to hell, and delivered them into chains of darkness, to be reserved unto judgment, the word that he uses for “hell” is “Tartarus”, and this is the only place in the Bible where it is ever found. It refers to the lowest regions of hell where the devils are tormented.
However, people do not generally express any sympathy for the devils’ suffering forever. After all, they rejected the greatest light of all - they’re the ongoing cause of all our misery - we see them (and I think rightfully so) as deserving everything they’ve got coming.
Given that the Bible says they’ll be tormented forever (despite the Bible’s silence on how they manage to avoid annihilation), I would see this as a case of arguing from the greater to the lesser - if the angels (which do not even have the breath of God to secure their immortality) will eternally suffer, then how much more confident should we be that humans who do bear His eternal image will as well?
As for why there is no redemption for them, I’d go back to that part about them having rejected the greatest light of all. The more light that one rejects, the more hardened they become against repentance. Among men, if someone rejects a limited amount of gospel light, we can reason that the same person, if confronted with greater light might reconsider and repent after all.
But as people receive greater and greater light, and stubbornly reject it, the become increasingly hardened until even the greatest light of all can no longer persuade them.
This is what had happened to the Pharisees in Matthew 12 who saw Jesus performing miracles that only the Spirit of God could have enabled - and the Spirit convicted them about the reality of Who Jesus was - and they quenched it, hardening themselves into a state of intractable irrepentance - hardened beyond pardon - not because of God’s limited ability to forgive, but because of their seared consciences that were no longer able to repent. It’s what Jesus called having blasphemed everything the Holy Spirit had revealed to them about Who Jesus really was. It is the sin of an antichrist - someone who has been given the greatest possible light, and they’ve turned from even that!
And once someone - whether man or angel - has sinned against the greatest possible light…well, where is there left to go from there? There was never any redemption available to the unrepentant.
I hope this helps you make sense of this question.