It is basic knowledge that PATH is used by a command interpreter to locate the pathname of binaries. This is true for Window's cmd.exe as well. I never heard of a system where locating files for execution was performed by a kernel.
newfstatat(AT_FDCWD, ".", {st_mode=S_IFDIR|0700, st_size=4096, ...}, 0) = 0
newfstatat(AT_FDCWD, "/usr/local/sbin/cat", 0x7fffcec2f3b8, 0) = -1 ENOENT (No such file or directory)
newfstatat(AT_FDCWD, "/usr/local/bin/cat", 0x7fffcec2f3b8, 0) = -1 ENOENT (No such file or directory)
newfstatat(AT_FDCWD, "/usr/sbin/cat", 0x7fffcec2f3b8, 0) = -1 ENOENT (No such file or directory)
newfstatat(AT_FDCWD, "/usr/bin/cat", {st_mode=S_IFREG|0755, st_size=68536, ...}, 0) = 0
Also true for MS/PC-DOS... which also holds the distinction of having some rare "truly monolithic" API-compatible variants that put the kernel, drivers, and shell in a single binary, so that may satisfy your criteria.
> If the file argument contains a slash character, the file argument shall be used as the pathname for this file. Otherwise, the path prefix for this file is obtained by a search of the directories passed as the environment variable PATH [...]
[1]: https://pubs.opengroup.org/onlinepubs/009695399/functions/ex...