A CHERI capability is stored in main memory but with the tag bit for that location set. The tags are stored in separate memory pages, also in main memory in current designs.

Maybe you've been confused by a description of how it works inside a processor. In early CHERI designs, capabilities were in different architectural processor registers from integers.

In recent CHERI designs, the same register numbers are used for capabilities and other registers. A micro-architecture could be designed to have either all registers be capability registers with the tag bit, or use register renaming to separate integer and capability registers.

I suppose a CHERI MCU for embedded systems with small memory could theoretically have tag pages in separate SRAM instead of caching main memory, but I have not seen that.