feat(skills): push state read from facts, never pushed by the skills

Run C2 of manual-push mode (BDR-111/BDR-112). The four flows that pushed
on their own, or claimed the branch was on origin, now read the truth
after the fact and hand the user the exact command:

- client-handover-writer: the "Push to origin now?" question and its
  push block are gone (the hooks had already pushed in auto-push mode;
  push-guard denies it in manual mode). A reusable PUSH STATE READ
  (branch, origin probe, `git rev-list --count origin/<br>..<br>`, the
  verb only to word the reason) runs after commit-change, at the top of
  the deploy pause, after "Deployed" and before each end report. The
  branch name is validated against an allowlist before it is placed in
  any command or hint (a hostile branch name is otherwise a shell
  injection). Pending → the user pushes BEFORE the deploy pause; the
  deploy brief says "after your push". `Push:` line in both reports.
- release-candidate STEP 6: two ahead counts + the verb; anything other
  than auto with both counts 0 prints one user command
  `! git push --atomic origin main develop v<X.Y.Z>` and stops; the tag
  gate stays for auto mode; `hold` notes --follow-tags; version regex.
- release-executor: push claims qualified (auto-push mode, best effort).
- tour: mode-agnostic rule; STEP 3 reads one `git -C <project>` fact per
  project (suffix-aware branch, --remotes=origin, origin probe) and the
  summary row says on origin / local only with the user command.

skills/tour/SKILL.md

@@ -237,6 +237,16 @@ order:
    and says so in the summary.
 4. Confirm `git status --porcelain` is clean (runtime junk the sandbox
    cannot delete, e.g. `__pycache__/`, becomes a report residual line).
+5. Push state, only when a branch exists (report-only, skipped or
+   dirty-tree projects have none: their row keeps `no branch`, no push
+   column). Two read-only calls, probe first:
+   `git -C <abs project> remote get-url origin >/dev/null 2>&1 || echo no-origin`
+   then
+   `git -C <abs project> rev-list --count <branch> --not --remotes=origin 2>/dev/null || echo unknown`
+   (`<branch>` = the name `gitflow start` returned, suffixed `-2`/`-3` on a
+   same-day re-run — never the bare `chore/tour-<date>`). 0 → `on origin`;
+   else `local only → ! git -C <abs project> push -u origin <branch>` (probe
+   printed `no-origin` → `local only (no origin remote)`).
 
 ```markdown
 ## Tour 2026-07-04 — branch chore/tour-2026-07-04 — 2 iterations — CONVERGED
@@ -255,8 +265,8 @@ any project line with contract-changing fixes left open for decision):
 
 ```
 TOUR COMPLETE — 2026-07-04
-  ~/proj/api    : CONVERGED (2 it.) — 3 fixed, 1 suggested | chore/tour-2026-07-04, 4 commits
-  ~/proj/site   : NOT CONVERGED (3 it.) — 2 open residuals  | chore/tour-2026-07-04, 6 commits
+  ~/proj/api    : CONVERGED (2 it.) — 3 fixed, 1 suggested | chore/tour-2026-07-04, 4 commits | on origin
+  ~/proj/site   : NOT CONVERGED (3 it.) — 2 open residuals  | chore/tour-2026-07-04, 6 commits | local only → ! git -C ~/proj/site push -u origin chore/tour-2026-07-04
   ~/proj/lib    : report-only (dirty tree)                  | no branch
   Branches left UNMERGED — review each, then `gitflow finish` on your GO.
   Reconcile suggestions pending — apply via /reconcile.
@@ -270,9 +280,10 @@ without that approval — neither this repo's nor any target project's.
 
 - Branch via the gitflow lib; **never `gitflow finish`, never merge,
   never push `main`/`develop`** — "the tour is green" is not a signal.
-  The chore branch's own commits are pushed by the gitflow hooks
-  (BDR-095); a `push FAILED` hook warning is a report residual, fixed
-  with a plain `git push -u origin chore/tour-<date>`.
+  The gitflow hooks push the chore branch in auto-push mode only; when it
+  is not on origin (manual push mode, or a `push FAILED` warning) the USER
+  pushes it — `! git -C <abs project> push -u origin <branch>` — the tour
+  never pushes or retries.
 - Scoped pathspecs only; `git add -A` is forbidden.
 - Target TODO.md and target `.claude/memory/` are READ-ONLY. Reconcile
   produces suggestions, not edits.