If we want to understand the text, we have to read the text as it was written in the context of what it says, and not superimpose our own later theological concepts upon it.
In Hebrew, there is no "heaven", there is only ha'shamayim, which is "the skies" (it is a dual plural).
Nor is there any "Hell". "Hell" is a word from Norse cosmology that means the underworld, a place of dishonor. To the Norse, we live in Midgard: Middle Earth. The valorous dead go to Asgard - the overworld of the gods and live in the hall of valor there - Valhallah - while the dishonored dead descend to Hel, below Midgard, where they dwell in a degree of shame. That's where we get the word "Hell", and the concept of "Hell" as a place for the damned. But the Hebrew does not contain this concept. Rather, the Hebrew is Sheol, which is simply the place to which the spirits (not souls) of the dead depart.
Also, while we see things in terms of a "soul" that detaches from the body, again, that is not what the Hebrew Bible says. In Hebrew, "breath" and "spirit" are one word and one and the same thing. It is the breath that comes from God and animates life, and the breath that departs at death (for Sheol). The word we translate as "soul" in Hebrew is really literally the word "breather". A living body is a breather - a soul. When it dies, the breath/spirit is withdrawn and the body falls back to the dust of the earth whence it comes. The spirit proceeds to Sheol.
Now then, in the older Hebrew Scripture, there is no sense of the punishment of souls in Sheol. Hebrew tradition contained it, but it wasn't written into Scripture until hinted at in the late books of the Old Testament (which are not in the Protestant Bible), and not fully revealed until Christ. It is Christ who divides Sheol (translated into Greek as "Hades" and, unfortunately, into English as "Hell") into Gehenna - a parched prison of fire and torment, where spirits go "until the last penny is paid" - and Paradise, where he promised the "good thief" dying alongside him he would be that day. Apparently the "Jewish section" of Paradise is where Abraham is, as the good dead such as Lazarus went to Abraham's bosom.
Now, if one examines the Jewish traditions for clarity, one discovers that Gehenna is purgatorial in nature. Jewish tradition is that spirits of sinners descend to Gehenna where they are purged in fire, and then most of them eventually pass to Gan Eden, which is the Hebrew for Paradise. In other words, if we're going to insist on incorporating Western linguistic structures into our translations, "Hell" is Sheol, "Heaven" is Paradise or Gan Eden, and Gehenna is "Purgatory". That fits the Jewish belief.
But, again, in the Old Testament, the dead never go up into the sky, they go into Sheol.
And actually, if one reads carefully, the dead do not go into Heaven in the New Testament either, at least not permanently. Revelation is the clearest about this.
Read carefully what happens: as the world ends, everybody is resurrected bodly - brought forth out of Hades ("Hell") to stand before the judgment seat. The City of God comes DOWN out of the sky ("Heaven") to earth and replaces the old Jerusalem and old earth that has passed away. Those who pass judgment then walk through the gates of the City of God, which is not "up there" but actually right down here on the earth, to live with with.
Those who are rejected are thrown into the Lake of Fire, to die again: the second death. But note that Hades/Hell/Sheol has itself been thrown into the Lake of Fire, and death also...which means that the second death is IT - burnt up, gone for good, done.
There is a long tradition of saying that one burns forever in the Lake of Fire, but the text does not actually SAY that. What it says is that the lake burns forever (just as the fires of Gehenna never were quenched and worm never ceased). What it does NOT say is that those thrown into that everlasting lake of fire continue to "live" in a spiritual sense. It says, rather, that they die.
The more natural read of that is that they are completely destroyed and gone for good, not that they linger, dead but alive. However, the Christian tradition is that they just burn there, dead but somehow alive also, in death, forever and ever.
That is a very long held and ancient belief. But it's not actually what the Scripture SAYS. It's an interpretation of the second death, and an elision of the everlasting nature of the fire with the thought that the life, too, in the fire is everlasting.
So, when Saul consulted the Witch of Endor, he was breaking the commandment of YHWH against seeking to communicate with the dead by way of a medium. He did successfully communicate with the dead, specifically with the spirit of Samuel, from Sheol. Samuel was not pleased with Saul, and gave him dire words of doom.
Saul died the next day, laden with sins, and then, following Jewish eschatology, descended to Gehenna. How long he stayed in Gehenna, and whether he crossed over into Gan Eden ever, or will pass judgment at the end of the world, Scripture does not say. We can only speculate, and who are we to dare to do so?