It is my understanding that ". . .
saints which slept arose, And came out of the graves after his resurrection, . . ." were not yet resurrected to immortality as Jesus was. They will receive that at time of the Millennium per Revelation 20:6.
Those were not people raised before the resurrection of Christ, like the son of Nain's widow.
They are raised
after and by Christ's resurrection.
And so the following applies to them:
Rom 6:4 Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life.
Rom 6:5 For if we have been planted together in the likeness of his death, we shall be also in the likeness of his resurrection:
[...]
Rom 6:8 Now if we be dead with Christ, we believe that we shall also live with him:
Rom 6:9 Knowing that Christ being raised from the dead dieth no more; death hath no more dominion over him.
Theirs was an eternal resurrection.
Indeed, he thereupon
led captivity captive, When he ascended up on high.
Those people, along with the souls in Abraham's bosom, were taken up.
the first resurrection has more than one phase, just like a harvest: firstfruits, harvest, gleanings.
That's why we only read of
the first resurrection at the beginning of the millennial kingdom, once the gleanings are in.
It's the one resurrection unto life, with the fruits coming in in three installments.
They will receive the kingdom at that time (of the kingdom) yes, but the eternal resurrection is theirs already.