The shell, not the Linux kernel, is responsible for searching for executables in PATH!
I mean, no shit, Sherlock? the exec family of system calls requires a path to a file, not a filename with an implicit path from the environment, of course the PATH is handled by the shell.
All members of the exec family of system calls, which consists of only two syscalls, namely, execve(2) and execveat(2), literally have the envp parameter which is supposed to have all the environment variables for the process.
Now, the semantics of this parameter is that kernel does not use it for path resolution when searching for the executable — but it could.
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I mean, no shit, Sherlock? the exec family of system calls requires a path to a file, not a filename with an implicit path from the environment, of course the PATH is handled by the shell.
All members of the exec family of system calls, which consists of only two syscalls, namely, execve(2) and execveat(2), literally have the envp parameter which is supposed to have all the environment variables for the process.
Now, the semantics of this parameter is that kernel does not use it for path resolution when searching for the executable — but it could.