Where do the souls that worshiped Kelemvor go

Discussion from 2010 suggests the wall is still there, and unbelievers are on a timer before they're cemented into the wall of the faithless.

Quoth:

It's still there until they specifically say it's not. We've been told to assume that unless something is described as different or gone, then it's still there.

Details of the wall:

Some minimal amount of real worship is required to initiate a patron relationship with a god. Without a patron, no god can claim you, so you are stuck in the Fugue. The servitors of any god who is not your patron cannot even see you, speak to you or interact with you in anyway. After a time, if no god comes to collect you, you feel the siren tug of Kelemvor's city calling to you to come for judgment.

The faithless begin to petrify and are tossed onto the wall. There is a moss that acts like a mortar that is corrosive and breaks down the substance of the petitioner body. Eventually the petitioner body is eaten away.

Moreover, there seems to be discussion of discussion of the wall in 4e fiction:

The wall was also mentioned in 4e novels (Edge of Chaos briefly mentions it IIRC)

On the other hand, heroes of shadow has worked out the Keeper of the Everflow ED. While the Heroes of X books are certainly not FR, the wall of the faithless can trivially equate to the raven queen stealing souls for her afterlife and Keepers can exist trying to restore the "natural" order of things.

Short answer: Yes. A soul consumed in a phylactery avoids any afterlife, and once destroyed after 24 hours it is gone completely.

With the religious structure in Forgotten Realms, any type of afterlife is depending on the Deity the character worships. To the point that if the character does not worship any kind of Deity in the Forgotten Realms setting, then divine spells to bring the character back from the dead are not effective, and the character's soul is supposed to sit in a kind of limbo for the rest of existence.

Also, the Imprisonment spell traps both body and soul, so it's better to think of the character being transported to another realm. With both body and soul intact and still connected, the character should still have awareness of their surroundings. In this case, their existence is now inside the Lich's phylactery.

There is no source that describes any specifics about what a creature experiences inside a phylactery. Whatever the character perceives in there is up to the creativity of the DM and the player.

However, since the soul has to be free to be delivered to their Deity to experience an afterlife, the character wouldn't experience that. While in the phylactery, the character doesn't experience an afterlife. After that 24 hour period, the soul is destroyed, not transported to their deity to experience an afterlife.