In 5e, souls become petitioners
Morte's Planar Parade, a companion to the Monster Manual, explains about Petitioners, which seems to be the default state of being for souls after arrival on their alignment matched plane, p. 4:
Death and the Planes
Mortals that die eventually have their souls return as petitioners in far-flung reaches of the Outer Planes. There, they manifest as idealized versions of themselves. These forms might be similar to the forms they had in life or be those of entirely different creatures.
Petitioners are former mortals. They've lived, ceased living, and now exist on the Outer Planes. They typically inhabit a plane that shares their alignment or the realm of a deity they worship.
This does not actually define a creature type. The book lists, ghost petitioners, berserker petioners, and commoner petitioners, even animal, flumph and beholder petitioners.
However they would not usually become angels, archons, modrons or slaadi that inhabit those planes.
Good aligned planes (Mount Celestia, Elysium, Arborea)
In 5e, Angels are not created from mortal souls, but from the astral essence of benevolent gods (MM, p. 14)
Shards of the Divine. Angels are formed from the astral essence of benevolent gods and are thus divine beings of great power and foresight.
Likewise, Archons are not described as made from the soul of mortals, but as created by the powers of order and benevolence (Morte's Planar Parade, p. 16; although it might still be possible that these powers create them by transforming mortal souls):
Archons are denizens of the Seven Heavens of Mount Celestia. Created by the powers of order and benevolence, archons defend their home from fiendish incursions and safeguard those threatened by wicked forces
Mechanus
And likewise, Modrons, the primary inhabitants of Mechanus are not described as being made from mortal souls but created by Primus (MM, p. 224; again one might not neccesarily exclude the other here):
Cogs of the Great Machine. If a modron is destroyed, its remains disintegrate. A replacement from the next lowest rank then transforms in a flash of light, gaining the physical form of its new rank. The promoted modron is replaced by one of its underlings in the same manner, all the way to the lowest levels of the hierarchy. There, a new modron is created by Primus, with a steady stream
of monodrones leaving the Great Modron Cathedral on Mechanus as a result.
Limbo
Lastly, the Slaadi of Limbo were spawned by the Spawing Stone, not created from mortal souls, and proliferate by implanting and transforming humanoids:
The foremost inhabitants of this inhospitable plane are the
toad-like slaadi. [...] Primus's creation had an unforeseen
side effect: the chaotic energy absorbed by the stone
spawned the horrors that came to be known as slaadi.
Sages refer to Primus's massive creation as the Spawning Stone for this reason. [...] Slaadi have horrific cycles of reproduction. Slaadi reproduce either by implanting humanoid hosts with eggs or by infecting them with a transformative disease called chaos phage.