IIUC everything in the observable universe is sufficiently far away from anything else that any causal relationship with anything is either from before inflation or within the universe we can observe.
And given how the existence of matter seems to be rather connected to time, it self a by product of interaction, it seems to follow that there is, relatively speaking, nothing beyond the horizon.
>> IIUC everything in the observable universe is sufficiently far away from anything else that any causal relationship with anything
I don't think that is correct. Suppose you have a particle that is very very near the horizon. This particle has its own observable universe and we are at the edge of its horizon. Now, this particle can have casual contact with the other parts of the universe (the parts beyond). But by the time the interaction takes place, it has already slipped out of our horizon. So from the perspective of the particle casual contact is possible. But from our perspective: Not even a chance to detect this interaction.
To be honest, that question never made any sense to me, because this whole discussion is merely about refining a semantic detail of the common word "existing". It says nothing about the particle itself, but just about our language.
For me, a far more interesting question is: Is it relevant? (for science?)
And the answer is: As long as it doesn't interact in any way with us, it is certainly not relevant whatsoever.
There is the observable universe and there are good reasons to believe that there is "some universe" beyond the observable universe. The observable universe is finite, the reason for that is the geometry of spacetime and the consequences of it (cosmological horizon/particle horizon). But I would not make absolute statements about what lies beyond the horizon(s), since there is (and can be) no data that would justify a statement about the infinity of space or the falsification of it.