There is one stack, the normal program stack that's normal main memory.
> capability pointers
If you use pure-capability CHERI C/C++ then there is only one type of pointer to manage; they just are implemented as capabilities rather than integers. They're also just extensions of the existing integer registers; much as 64-bit systems extend 32-bit registers, CHERI capability registers extend the integer registers.
> requires microarchitectural support for a tag storage memory
Also true of MTE?
> your memory operations also need to provide a pointer to a capability object stored in the capability store
There is no "capability object stored in the capability store". The capability is just a thing that lives in main memory that you provide as your register operand to the memory instruction. Instead of `ldr x0, [x1]` to load from the address `x1` into `x0`, you do `ldr x0, [c1]` to load from the capability `c1`. But `c1` has all of the capability; there is no indirection. It sounds like you are thinking of classical capability systems that did have that kind of indirection, but an explicit design goal of CHERI is to not do that in order to be much more aligned with contemporary microarchitecture.
> The capability store is literally a separate bus and memory that isn't accessible by programs,
As above, there is no separate bus, and capabilities are not in separate memory. Everything lives in main memory and is accessed using the same bus. The only difference is there are now capability tags being stored alongside that data, with different schemes possible (wider SRAM, DRAM ECC bits, carving out a bit of main memory so the memory controller can store tags there and pretend to the rest of the system that memory itself stores tags). To anything interacting with the memory subsystem, there is one bus, and the tags flow with the data on it.