feat: add EditEventScreen with calendar and chat mode support

Add a unified event editor that works in two modes:
- Calendar mode: Create/edit events directly via EventService API
- Chat mode: Edit AI-proposed events before confirming them

The chat mode allows users to modify proposed events (title, time,
recurrence) and persists changes both locally and to the server.

New components: DateTimePicker, ScrollableDropdown, useDropdownPosition
New API: PUT /api/chat/messages/:messageId/proposal

packages/shared/src/utils/dateHelpers.ts

@@ -34,3 +34,15 @@ export function getDay(
   result.setHours(hour, minute, 0, 0);
   return result;
 }
+
+/**
+ * Check if an event spans multiple days.
+ * Compares dates at midnight to determine if start and end are on different calendar days.
+ */
+export function isMultiDayEvent(start: Date, end: Date): boolean {
+  const startDate = new Date(start);
+  const endDate = new Date(end);
+  startDate.setHours(0, 0, 0, 0);
+  endDate.setHours(0, 0, 0, 0);
+  return startDate.getTime() !== endDate.getTime();
+}