feat(calendar): internal event store with FullCalendar UI and CalDAV push sync

- AI calendar tools now always available (moved from _CALDAV_TOOLS to _CORE_TOOLS);
  create/list/search/update/delete events go through the internal DB store first,
  with fire-and-forget CalDAV push sync when the user has CalDAV configured
- Add EventEntry interface and typed API helpers (listEvents, createEvent,
  getEvent, updateEvent, deleteEvent) to client.ts
- Install @fullcalendar/vue3, daygrid, timegrid, interaction, core packages
- Add EventSlideOver.vue: create/edit/delete slide-over with title, start/end,
  all-day toggle, location, description, color picker, and project selector
- Add CalendarView.vue: month/week/day FullCalendar with drag-drop and resize
  wired to PATCH /api/events/:id; click empty date opens create slide-over
- Wire /calendar route, Calendar nav link in AppHeader, g+l keyboard shortcut

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

frontend/src/api/client.ts

@@ -516,3 +516,69 @@ export async function apiStreamPost(
     }
   }
 }
+
+// ---------------------------------------------------------------------------
+// Calendar events
+// ---------------------------------------------------------------------------
+
+export interface EventEntry {
+  id: number;
+  uid: string;
+  title: string;
+  start_dt: string;
+  end_dt: string | null;
+  all_day: boolean;
+  description: string;
+  location: string;
+  color: string;
+  recurrence: string | null;
+  caldav_uid: string;
+  project_id: number | null;
+  user_id: number;
+  created_at: string | null;
+  updated_at: string | null;
+}
+
+export interface EventCreatePayload {
+  title: string;
+  start_dt: string;
+  end_dt?: string;
+  all_day?: boolean;
+  description?: string;
+  location?: string;
+  color?: string;
+  recurrence?: string;
+  project_id?: number;
+}
+
+export interface EventUpdatePayload {
+  title?: string;
+  start_dt?: string;
+  end_dt?: string;
+  all_day?: boolean;
+  description?: string;
+  location?: string;
+  color?: string;
+  recurrence?: string;
+  project_id?: number;
+}
+
+export async function listEvents(from: string, to: string): Promise<EventEntry[]> {
+  return apiGet<EventEntry[]>(`/api/events?from=${encodeURIComponent(from)}&to=${encodeURIComponent(to)}`);
+}
+
+export async function createEvent(payload: EventCreatePayload): Promise<EventEntry> {
+  return apiPost<EventEntry>('/api/events', payload);
+}
+
+export async function getEvent(id: number): Promise<EventEntry> {
+  return apiGet<EventEntry>(`/api/events/${id}`);
+}
+
+export async function updateEvent(id: number, payload: EventUpdatePayload): Promise<EventEntry> {
+  return apiPatch<EventEntry>(`/api/events/${id}`, payload);
+}
+
+export async function deleteEvent(id: number): Promise<void> {
+  return apiDelete(`/api/events/${id}`);
+}