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Wiki: shift.md (site-wide single-open + gate; superseded per-operator note),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.

apps/web/src/lib/use-shift.ts

@@ -0,0 +1,42 @@
+import { useQuery } from "@tanstack/react-query";
+import { fetchShift, type ShiftStatus } from "../api.js";
+import { qk } from "./query.js";
+
+// Shared shift status for the whole app — the header control, the booth screen's
+// per-shift log scope, and the pay/exit modal's gate all read this one Query so
+// they never disagree about whether a shift is open and whose it is. A shift is a
+// SITE-WIDE single-open accountability period (at most one open at a time). The WS
+// invalidates qk.shift on shift_open/shift_z_report/cash_movement, so this stays
+// live without polling. See wiki/concepts/shift.md.
+
+export interface ShiftState {
+  /** Raw status from the server (null while loading / on error). */
+  status: ShiftStatus | undefined;
+  /** Is ANY shift open site-wide? */
+  isOpen: boolean;
+  /** Is the open shift the logged-in operator's (so they may close it / operate)? */
+  isMine: boolean;
+  /** A shift is open but belongs to someone else — this operator is blocked. */
+  blockedByOther: boolean;
+  /** ISO start of the open shift, for scoping the per-shift log. */
+  startedAt: string | null;
+  /** Whoever holds the open shift (for "held by X" messaging). */
+  heldBy: string | null;
+  isLoading: boolean;
+}
+
+export function useShift(): ShiftState {
+  const q = useQuery({ queryKey: qk.shift, queryFn: fetchShift });
+  const s = q.data;
+  const isOpen = s?.open != null;
+  const isMine = s?.isMine ?? false;
+  return {
+    status: s,
+    isOpen,
+    isMine,
+    blockedByOther: isOpen && !isMine,
+    startedAt: s?.open?.startedAt ?? null,
+    heldBy: s?.open?.operator ?? null,
+    isLoading: q.isLoading,
+  };
+}