Jesus was talking about the raising of the dead in John 5. That’s when he said eternal life comes, a future thing.
Luke 20
34Jesus replied, “The people of this age marry and are given in marriage.
35But
those who are considered worthy of taking part in the age to come and in the resurrection from the dead will neither marry nor be given in marriage,
36and
they can no longer die; for they are like the angels. They are God’s children, since they are children of the resurrection.
So as to whether or not there is immortality right now, I don’t think so. Consider what Paul said too:
1 Corinthians 15
52in a flash, in the twinkling of an eye,
at the last trumpet. For the trumpet will sound, the dead will be raised imperishable, and we will be changed.
53For the perishable must clothe itself with the imperishable, and the mortal with immortality.
54When the perishable has been clothed with the imperishable, and the mortal with immortality, then the saying that is written will come true: “Death has been swallowed up in victory.”
So a question of reflection:
Have you been raised imperishable and clothed with immortality at the last trumpet? Wouldn’t it follow that before the last trumpet one is perishable and mortal?