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Wiki: shift.md (site-wide single-open + gate; superseded per-operator note),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

@@ -1,5 +1,5 @@
 import type { FastifyInstance } from "fastify";
-import { desc, ledgerEvents, type Db } from "@parking/db";
+import { desc, gte, ledgerEvents, type Db } from "@parking/db";
 import { requireRole } from "../auth.js";
 import type { EventLog } from "../event-log.js";
 
@@ -17,12 +17,22 @@ export async function eventRoutes(
   const guard = requireRole("admin", "operator", "cashier", "readonly");
 
   // Recent events, newest first. `limit` caps the page (default 100, max 1000).
-  app.get<{ Querystring: { limit?: string } }>(
+  // Optional `since` (ISO) scopes the page to events at/after that instant — the
+  // booth passes the current shift's start so the live feed shows ONLY this shift's
+  // activity (logs are per-shift, not all history). See wiki/concepts/shift.md.
+  app.get<{ Querystring: { limit?: string; since?: string } }>(
     "/api/events",
     { preHandler: guard },
     async (req) => {
       const limit = Math.min(Math.max(Number(req.query.limit) || 100, 1), 1000);
-      const rows = db.select().from(ledgerEvents).orderBy(desc(ledgerEvents.index)).limit(limit).all();
+      const since = (req.query.since ?? "").trim();
+      const rows = db
+        .select()
+        .from(ledgerEvents)
+        .where(since ? gte(ledgerEvents.occurredAt, since) : undefined)
+        .orderBy(desc(ledgerEvents.index))
+        .limit(limit)
+        .all();
       return { events: rows };
     },
   );