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Wiki: shift.md (site-wide single-open + gate; superseded per-operator note),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

@@ -317,8 +317,12 @@ export function deletePermit(id: string): Promise<void> {
 // --- Shifts ---------------------------------------------------------------
 
 export interface ShiftStatus {
+  /** The requesting (logged-in) operator. */
   operator: string;
-  open: { startedAt: string } | null;
+  /** The SINGLE site-wide open shift (startedAt + whose), or null if none open. */
+  open: { startedAt: string; operator: string | null } | null;
+  /** True iff the open shift belongs to the requesting operator (can close it). */
+  isMine: boolean;
   /** Live physical drawer balance (cash payments + cash movements). */
   drawerMinor: number;
   currency: string | null;
@@ -394,9 +398,16 @@ export function fetchOccupancy(): Promise<Occupancy> {
 export type { LedgerEvent } from "@parking/shared";
 
 /** Recent ledger events, newest first (default 100, max 1000). Used for the
- *  booth feed's initial load; live updates then arrive over the WS. */
-export function fetchEvents(limit = 100): Promise<{ events: import("@parking/shared").LedgerEvent[] }> {
-  return apiFetch(`/api/events?limit=${limit}`);
+ *  booth feed's initial load; live updates then arrive over the WS. `since` (ISO)
+ *  scopes to events at/after that instant — the booth passes the current shift's
+ *  start so the feed shows ONLY this shift's activity. */
+export function fetchEvents(
+  limit = 100,
+  since?: string,
+): Promise<{ events: import("@parking/shared").LedgerEvent[] }> {
+  const qs = new URLSearchParams({ limit: String(limit) });
+  if (since) qs.set("since", since);
+  return apiFetch(`/api/events?${qs.toString()}`);
 }
 
 // --- Booth: session lookup, payment, exit ---------------------------------