Are the Material Planes comprising the various campaign settings surrounded by a shared set of outer planes?


I’m working on an extra-planar supplement for DM’s Guild, and it got me wondering:

Is the 5e cosmological model that the material planes are comprised of all DnD settings, official and otherwise (Forgotten Realms, Eberron, and other published or future campaign worlds), surrounded by the outer planes which are common to all of them?

If this is the case, would that mean that the outer planes are comprised of souls from realms other than the players’ native world? Would a party who ventures there meet souls originally from Eberron, Athas, Greyhawk, etc.?

On the other hand, it’s possible I’m confusing my editions, and in 5e each campaign world has its own greater cosmology. In that case, are the outer planes unique to the Forgotten Realms, and does Eberron, for example, have its own set of outer planes?