Thanks for taking the extra time making me consider dropping the term "kernel". But I need a term wich reflects my efforts. So I fed your description at the end into ChatGPT, asking for a one-word description. This is what it came up with:

Paravirtualized – commonly used when an interface mimics low-level system behavior but redirects to a host implementation; this fits your syscall-level emulation.

Interposed – describes the interception and redirection of system calls or API behavior.

Emulated – broad but accurate; emphasizes imitation of behavior at the syscall layer.

Rehosted – suggests the POSIX environment has been adapted to a different host OS.

Substituted – captures the idea of replacing one system mechanism with another.

Intercepted – emphasizes the capture and redirection of syscalls.

Translated – suitable if there's transformation between POSIX calls and Windows kernel APIs.

Adapted – highlights compatibility through minimal changes.

Bridged – suggests a connection or interface between incompatible systems.

Virtualized – somewhat general, but appropriate if the environment feels like a lightweight VM layer.

Interesting, but not very creative. Something like Ted Nelson's "transclusion". Suggestions? Anyone?