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Wiki: shift.md (site-wide single-open + gate; superseded per-operator note),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

@@ -11,9 +11,16 @@ import type { EventLog } from "./event-log.js";
 // See wiki/concepts/shift.md.
 
 export class ShiftAlreadyOpenError extends Error {
-  constructor(operator: string) {
-    super(`operator ${operator} already has an open shift`);
+  /** The operator who currently holds the open shift (may be someone else). */
+  readonly heldBy: string;
+  constructor(operator: string, heldBy: string) {
+    super(
+      heldBy === operator
+        ? `operator ${operator} already has an open shift`
+        : `another operator (${heldBy}) has an open shift; only one shift may be open at a time`,
+    );
     this.name = "ShiftAlreadyOpenError";
+    this.heldBy = heldBy;
   }
 }
 export class NoOpenShiftError extends Error {
@@ -22,6 +29,14 @@ export class NoOpenShiftError extends Error {
     this.name = "NoOpenShiftError";
   }
 }
+/** Thrown by the booth money path when NO shift is open site-wide — an operator
+ *  must open a shift before any payment/exit can be attributed to a shift. */
+export class NoShiftOpenError extends Error {
+  constructor() {
+    super("no shift is open — open a shift before processing tickets");
+    this.name = "NoShiftOpenError";
+  }
+}
 
 export interface ShiftReport {
   readonly operator: string;
@@ -82,6 +97,31 @@ export class ShiftService {
     return last && last.type === "shift_open" ? last : null;
   }
 
+  /**
+   * The SINGLE site-wide open shift, or null. A shift is a site-wide accountability
+   * period: at most ONE may be open at a time (so booth takings are unambiguously
+   * attributed to one operator). It's open iff the most recent shift event on the
+   * whole chain is a `shift_open` (the matching `shift_z_report` hasn't been
+   * appended yet). Returns that row so callers can read its operator/startedAt.
+   */
+  currentOpenShift() {
+    const rows = this.#db
+      .select()
+      .from(ledgerEvents)
+      .orderBy(ledgerEvents.index)
+      .all()
+      .filter((r) => r.type === "shift_open" || r.type === "shift_z_report");
+    const last = rows[rows.length - 1];
+    return last && last.type === "shift_open" ? last : null;
+  }
+
+  /** Require an open shift for the booth money path; returns it or throws. */
+  requireOpenShift() {
+    const open = this.currentOpenShift();
+    if (!open) throw new NoShiftOpenError();
+    return open;
+  }
+
   /**
    * The physical drawer balance at `at`: a fold over the SIGNED chain BY TIME (not
    * by operator — a cash_movement is the admin's, not the shift operator's). Cash
@@ -149,7 +189,11 @@ export class ShiftService {
   /** Open a shift for the operator (explicit start). The opening float is auto-
    *  inherited from the chain = the drawer balance at the start instant. */
   async open(operator: string): Promise<{ startedAt: string; openingFloatMinor: number }> {
-    if (this.openShiftFor(operator)) throw new ShiftAlreadyOpenError(operator);
+    // Site-wide single-open invariant: refuse if ANY shift is open — whether this
+    // operator's own (double-open) or another operator's (handover not done). Only
+    // one accountability period at a time.
+    const current = this.currentOpenShift();
+    if (current) throw new ShiftAlreadyOpenError(operator, current.identity ?? operator);
     const startedAt = new Date().toISOString();
     const { balanceMinor: openingFloatMinor } = this.#drawerBalanceAt(startedAt);
     await this.#log.append({