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Wiki: shift.md (site-wide single-open + gate; superseded per-operator note),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

@@ -64,6 +64,15 @@ export function useLiveFeed(): void {
           void qc.invalidateQueries({ queryKey: qk.events });
           void qc.invalidateQueries({ queryKey: qk.occupancy });
           void qc.invalidateQueries({ queryKey: qk.activeSessions });
+          // A shift open/close (or a drawer movement) changes the header control
+          // state and the per-shift log window — refresh the shift status too.
+          if (
+            msg.event.type === "shift_open" ||
+            msg.event.type === "shift_z_report" ||
+            msg.event.type === "cash_movement"
+          ) {
+            void qc.invalidateQueries({ queryKey: qk.shift });
+          }
         } else if (msg.kind === "printer-status") {
           void qc.invalidateQueries({ queryKey: ["printers"] });
         }