refactor(core): remove hardcoded PATH reset

PATH='/bin:/usr/bin:/usr/local/bin' was intended as a security measure
against PATH injection. For a script invoked manually in the user's own
shell the benefit is marginal: if an attacker controls the user's PATH
they already have larger problems. The cost is real — tools installed
outside these three directories (Homebrew, Nix, ~/.local/bin) silently
fail, and the documented workaround of prepending a path at invocation
time does not work because the script overwrites PATH immediately on
startup.

Remove the PATH reset and all associated documentation. The remaining
hardening measures (unalias -a, hash -r, strict set -o flags, umask) are
retained.

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