feat: task 2.7 event picker (subscription driver)

- src/data/events.ts: useUserEvents() TanStack Query (5-min stale,
  sort -starts_at). EventSummary type is a Pick of EventRow.
- src/live/active-event.ts: useActiveEventOrchestration() returns the
  swap fn — unsubscribe previous + clearForEvent + subscribe new +
  applySnapshot on success + persist to localStorage. Out-of-order
  safety via per-call version counter. Plus readSavedActiveEventId().
- src/ui/components/event-picker.tsx: <EventPicker> dropdown.
  useState + click-outside; rows show name + date + discipline.
- src/live/index.ts: re-exports active-event helpers.
- src/routes/_authed/monitor.tsx: auto-select effect (one-shot via
  initializedRef, gated on events loaded + WS connected); renders
  <EventPicker> wired to setActiveEvent.

Deviations:
1. Vanilla div + useState dropdown instead of shadcn Popover —
   no new shadcn primitive add; easy to swap later for keyboard nav.
2. Auto-select gated on connectionStatus === 'connected' so the
   subscribe call gets the snapshot path (not 'not-connected').
3. Logout-clears-saved-event-id deferred to a small Phase 1.8
   follow-up; documented in task risks.

Bundle: 395KB / 120KB gz (~1KB up from 2.6).

src/routes/_authed/monitor.tsx

@@ -1,15 +1,45 @@
+import { useEffect, useRef } from 'react';
 import { createFileRoute } from '@tanstack/react-router';
+import { useUserEvents } from '@/data/events';
+import {
+  readSavedActiveEventId,
+  useActiveEventOrchestration,
+  useConnectionStore,
+  usePositionStore,
+} from '@/live';
 import { BasemapSwitcher } from '@/map/core/basemap-switcher';
 import { MapView } from '@/map/core/map-view';
 import { TrailsToggle } from '@/map/core/trails-toggle';
 import { MapPositions } from '@/map/layers/map-positions';
 import { MapTrails } from '@/map/layers/map-trails';
+import { EventPicker } from '@/ui/components/event-picker';
 
 export const Route = createFileRoute('/_authed/monitor')({
   component: MonitorPage,
 });
 
 function MonitorPage() {
+  const activeEventId = usePositionStore((s) => s.activeEventId);
+  const setActiveEvent = useActiveEventOrchestration();
+  const events = useUserEvents();
+  const connectionStatus = useConnectionStore((s) => s.status);
+  const initializedRef = useRef(false);
+
+  // Auto-select on first mount: prefer the previously-saved event id;
+  // otherwise the most recent. Gated on the WS being connected so the
+  // subscribe call doesn't immediately resolve with `not-connected`.
+  useEffect(() => {
+    if (initializedRef.current) return;
+    if (!events.data || events.data.length === 0) return;
+    if (connectionStatus !== 'connected') return;
+    initializedRef.current = true;
+
+    const saved = readSavedActiveEventId();
+    const target =
+      saved && events.data.some((e) => e.id === saved) ? saved : (events.data[0]?.id ?? null);
+    if (target) void setActiveEvent(target);
+  }, [events.data, connectionStatus, setActiveEvent]);
+
   return (
     // 3.5rem ≈ 56 px reserved for a future top-bar (Phase 3 chrome).
     // For now the parent _authed layout has no top-bar, so the map can
@@ -20,6 +50,12 @@ function MonitorPage() {
           UI controls. Floating cards positioned absolutely inside
           <MapView>'s wrapper.
         */}
+        <EventPicker
+          activeEventId={activeEventId}
+          onChange={(id) => {
+            void setActiveEvent(id);
+          }}
+        />
         <BasemapSwitcher />
         <TrailsToggle />
         {/*