According to this older post: https://security.stackexchange.com/a/174968/271114 Intel processors are stateless.
Nowadays a "CPU" is often a SOC integrating neural engines, GPUs, coprocessors, secure enclaves and more.
Other architectures like ARM64, RISC-V and POWER9 are also more common. Do they (or maybe others) keep state? Could malware hide in a modern SOC?