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

Makefile

@@ -0,0 +1,13 @@
+.PHONY: check gen hook
+
+## check   — verify repo self-consistency (syntax, exec bits, doc/code sync, smoke)
+check:
+	./scripts/check-sync.sh
+
+## gen     — regenerate code-derived doc sections + completion flags
+gen:
+	./scripts/gen-docs.sh
+
+## hook    — install the opt-in pre-commit hook (runs `make check`)
+hook:
+	./scripts/install-hooks.sh