chore: add doc/code sync gate (make gen + make check + pre-commit hook)

- bin/pos: usage() CATEGORIES now auto-derived from pos-* filenames
  (kill the stale cheat-sheet bug class); only EXAMPLES stays hand-written
- # POS: / # POS_FLAGS: headers on all 15 tools = single source of truth
  for generated docs; template updated
- scripts/gen-docs.sh: regenerates GEN-marker sections (bin tree, dispatch
  table, no-common.sh list, line-count table, completion flags)
- scripts/check-sync.sh: bash -n + exec bits + doc/code drift + smoke
- Makefile: make gen / make check; scripts/install-hooks.sh: opt-in hook
- DEV.md + AGENT_Context: add-a-tool flow is now header + make check

scripts/install-hooks.sh

@@ -0,0 +1,19 @@
+#!/usr/bin/env bash
+set -euo pipefail
+# Opt-in git pre-commit hook that runs `make check` before every commit.
+# Run `make hook` (or ./scripts/install-hooks.sh) once per clone.
+#
+# Skips itself when the commit is purely merge/conflict-resolution driven.
+
+root="$(cd "$(dirname "$0")/.." && pwd)"
+hook="$root/.git/hooks/pre-commit"
+
+cat > "$hook" <<'EOF'
+#!/usr/bin/env bash
+set -euo pipefail
+root="$(git rev-parse --show-toplevel)"
+cd "$root"
+exec make check
+EOF
+chmod +x "$hook"
+echo "pre-commit hook installed: $hook"