How much does semver make sense for an OS kernel? It makes more sense to split out function calls into families based on purpose and stability, and declare that this family of functions is stable, this family is not, and focus on keeping the kernel running in a stable fashion regardless of the declared version number.

If anything, that makes even more sense for a microkernel, with different function call families being provided by different servers.

Well technically yes, because of semver 2.0's rule #4: "Anything may change at any time. The public API should not be considered stable."

Prima facie no because semver requires MAJOR.MINOR.PATCH (even for PATCH == 0) and this is just MAJOR.MINOR.