Huawei design their own chips but I don't know if they designed their own core or not.
I thought they used ARM cores and GPUs and added some of their own logic around that.
But there are people with the ability to design CPU cores in China.
Designing your own CPU cores for the smartphone business makes zero sense from a business perspective. As of right now, Android does not support architectures outside of x86 and ARM, both proprietary IP. Sure, once upon a time it supported MIPS, but the maintainers officially dropped support in the later versions. Even Apple's iOS runs exclusively on ARM chips.
Introducing another architecture into the smartphone business would mean creating an entirely new technology stack from scratch. New OS, new development tools, and new app ecosystem. One company can't possibly do this alone. You would need to establish something like a standards body to coordinate all of the relevant parties.