feat(shift): site-wide single-open shift + booth money-path gate

A shift becomes a SITE-WIDE accountability period — at most one open at a
time — so every taking is unambiguously attributed to one operator. Login
stays decoupled from shifts (an operator can log in off-shift to review).

Backend:
- ShiftService.currentOpenShift()/requireOpenShift(); open() refuses when ANY
  shift is open and throws ShiftAlreadyOpenError{heldBy} (self vs. other).
- requireShift preHandler gates /api/pay, /api/exit, /api/voucher,
  /api/barrier/reopen → 409 {code:"no_shift"}; read-only lookups stay open.
- GET /api/shift/current returns site-wide {open:{startedAt,operator},isMine}.
- GET /api/events?since=<iso> for per-shift log scoping (db: re-export gte).

Frontend:
- Header shift button: open / close-mine / disabled-when-another-holds-it.
- Pay/exit modal gate banner (one-click open; "held by X" when another's);
  pay/exit/voucher disabled until this operator's shift is open.
- Active-Sessions barrier re-open gated the same way.
- Live feed scoped to the open shift's window; shared useShift() Query
  invalidated over the WS on shift_open/shift_z_report/cash_movement.
- sq/en strings for the control + gate.

Wiki: shift.md (site-wide single-open + gate; superseded per-operator note),
booth-console.md (header control + gate), log entry.

Verified: site-wide invariant + heldBy + handover + chain integrity on a
fresh migrated DB (11/11); db/server/web build clean.

wiki/concepts/booth-console.md

@@ -63,6 +63,26 @@ a right column with the **live event ticker**. Submitting/clicking a ticket open
 modal** (entry/duration/total, tender, voucher checkbox, entry/exit snapshots). All live-refreshed via
 the WS.
 
+## The shift control (header) + the booth gate
+
+The header carries a single **shift button** that expresses the [[shift|site-wide single-open
+shift]] (added 2026-06-18):
+
+- **No shift open** → "Open shift" (green, enabled).
+- **My shift open** → "Close shift" (red, enabled — signs + prints the Z-report).
+- **Another operator's shift open** → **disabled**, titled with who holds it. You can neither open
+  yours nor close theirs until they hand over.
+
+State comes from one shared Query (`useShift()` → `GET /api/shift/current`, returning `{ open:
+{startedAt, operator} | null, isMine }`); the WS invalidates it on `shift_open` / `shift_z_report` /
+`cash_movement`, so the button (and the per-shift log scope) update live without polling.
+
+The **booth screen gates on this**: the pay/exit modal shows an "open a shift" banner (with a
+one-click *Open shift now*) and disables pay/exit/voucher until **this operator's** shift is open;
+the Active-Sessions "Open barrier" is disabled the same way. The server enforces it regardless
+(`requireShift` 409 `no_shift`) — the UI just front-runs the rejection. The live feed is **scoped to
+the open shift's window** (empty when no shift is open). See [[shift]] for the rule and the routes.
+
 ## Dev notes
 - Vite proxies `/api/ws` (`ws: true`) to the backend; the backend's Origin allowlist must include the
   dev SPA origin (`WS_ALLOWED_ORIGINS=http://localhost:5173`). In production Fastify serves the SPA