Braythe and other cosmologies

Braythe is not just a new campaign world; it is an entire reality of its own. At the same time, it is not a complete cosmology. The dimension that is Braythe is like a reality bubble separated from other cosmologies, but with conduits leading into those other layers of existence.
This means that Braythe has no afterlife or elemental planes of its own. When a new world gets transported into the Braythian dimension, it is completely isolated from such planes. Only after a few days, new conduits open up, granting access to those other planes again.
Because of these conduits, Braythe can serve as a bridge between cosmologies: Travellers can reach alternate realities via a quick visit to one of the world-islands. It also implies that different versions of the afterlife or elemental planes are accessible. This could even go so far that two different versions of a deity have followers on one and the same world.

Braythe Cosmology by Heiner de Wendt

Gods and the world-islands

These properties of Braythe also define which deities can influence a world-island and build a followership. As long as there is a conduit to a certain god's home plane, the deity can be active here.
The gods that have been revered in the lands that now make up the new world usually still have an active presence after the recreation of the world. That is, as long as they have survived the apocalypse themselves.
Believers of a god seem to be (or create) conduits of their own. This means that a cleric or other spellcaster can access his or her god's powers even when journeying to other Braythian worlds. It also means that a god can at least temporarily access that new world. And if a cleric manages to convert some locals, the god's access to the world could very well become permanent.

Alternative interpretations

As with everything, it is up to the game master whether your version of Braythe fits the above description. Maybe the existing conduits only lead to one other cosmology, or new gods from other realities cannot access world-islands they didn't have access to before.

Isolation or full access?

It's recommended to allow most spells that require planar access, simply to make the game easier to handle for everyone. But that doesn't mean there's no room to play with the concept of conduits. Planar travel, for example, might only be possible if you find a nearby conduit that leads to the plane you want to reach. Access to Braythe from other planes could be restricted in a similar way. Summoning creatures might be limited to alternative lists for entities to be summoned, and so on.
These decisions are up to the game master, of course. Officially, there are no general restrictions to magic and planar travel in Braythe. Local effects due to a nearby conduit might affect these things, and other planes will only play a direct role in Braythe on rare occasions. As a GM, feel free to adapt these concepts to your style of play - just make sure you keep it consistent, so your players know what they are up to.