"what the characters inhabitating it are really?"
i actually really truly can't! as soon as you say "what are they really" the question becomes self-defeating and basically unanswerable.
i think i've elaborated on how i basically regard the meta before, ten million years ago and beyond, as being largely intuitive and impossible (and undesirable) to truly concretely pin down, though it has its own space and its own emotional continuity, but if you put five shotguns to my head, i'd say - they're figures of narrative, which i would distinguish from simply being "fictional constructs."
it doesn't feel right to me to say they're "souls of the afterlife" because there's an underpinning of umineko about a person's genuine soul, a genuine personhood, being impossible to capture in a single narrative or linear perspective, and this informs how their roles vary according to the needs of the gameboard, even down to the golden land itself, an obviously idealized space for everyone involved. but "fictional constructs" also feels too dismissive and belies the emotional weight and struggle we see even "piece-Ange" wrestle with. narrative shapes reality and all that - i think it's almost impossible for most humans to not filter reality through a narrative lens on some level, and in the case of ange, much of her struggle with lambda's temptation was about the option of sort of. the word escapes me. taking over beatrice's gameboard to center herself, or accepting her role in the "narrative" as a sacrifice to emotional spur assigned-protagonist battler onward.
the genuine internal life and sometimes agency of the pieces as such, struggling with their places within narrative, is what allows rika who is described as originally being a piece under the control of a game-master to ascend as a witch. but, that's still different from suggesting they're literally the souls of the real breathing human beings who died in the rokkenjima explosion, somehow actually literally put under the control of yasuda sayo in a magic purgatorial space.
even struggling to describe it as such feels insufficient and reductive, though. very deep and complicated, i tell you. lights pipe, kicks back in chair. falls over in chair and gets concussion, never speaks again.