> The kernel represents itself as a process (process zero)

This isn't true of any modern operating system. Kernel code isn't confined to a single process or even a limited number of processes. Transitioning to kernel mode doesn't necessitate switching to a dedicated process. Prior to the emergence of CPU speculative execution vulnerabilities, it was common for kernel code to be mapped directly into the virtual address spaces of userspace processes.

PID 0 is merely an implementation detail of the scheduler shared among many Unices. It doesn't function like a normal process, nor is it an accurate representation of how the large part of the kernel operates.