Inner vs outer shareable is not particularly relevant for applications - from the ARM ARM:
> This architecture assumes that all PEs that use the same operating system or hypervisor are in the same Inner Shareable shareability domain.
[PE = processing element - i.e. core]
i.e. if you a running a userspace program, all the cores are in the same shareability domain.
(I think your comments about LDAR/STLR are a response to 'adwn's sibling comment).
Eventual write propagation is a very basic liveness guarantee for systems with coherent caches. I'm pretty sure that the ARM architecture requires it for Observers with coherent caches, but event if not, it would be very surprising if a mainstream implementation didn't provide this guarantee.
Barrier instructions provide control of ordering relationships between accesses and when accesses complete, but I believe there is a guarantee that accesses eventually complete even without barriers.
(Also from the ARM ARM (B2.3.7), "complete" here means "visible to other cores": "Any read to the same Location by an Observer within the shareability domain will either Reads-from W1 or Reads-from a write that is Coherence-after W1.")
I'd be very interested to learn that ARM (or Ampere Altra) doesn't guarantee eventual write propragation, but that needs a better source than [2].