feat: add local schedule cache + periodic sync to CalendarScheduler

- New ScheduleCache class: maintains today's full schedule locally
- CalendarBridgeClient.getDaySchedule(): fetch all slots for a date
- Scheduler now runs two intervals:
  - Heartbeat (60s): existing slot execution flow (unchanged)
  - Sync (5min): pulls full day schedule into local cache
- Exposes getScheduleCache() for tools and status reporting

This enables the plugin to detect slots assigned by other agents
between heartbeats and provides a complete local view of the schedule.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

plugin/calendar/calendar-bridge.ts

@@ -169,6 +169,32 @@ export class CalendarBridgeClient {
     return this.sendBoolean('POST', url, body);
   }
 
+  /**
+   * Fetch the full day schedule for this agent.
+   *
+   * Unlike heartbeat() which only returns pending (NOT_STARTED/DEFERRED) slots,
+   * this returns ALL slots for the given date, enabling the plugin to maintain
+   * a complete local view of today's schedule.
+   *
+   * @param date  Date string in YYYY-MM-DD format
+   * @returns Array of all slots for the day, or null if unreachable
+   */
+  async getDaySchedule(date: string): Promise<CalendarSlotResponse[] | null> {
+    const url = `${this.baseUrl}/calendar/day?date=${encodeURIComponent(date)}`;
+    try {
+      const response = await this.fetchJson<{ slots: CalendarSlotResponse[] }>(url, {
+        method: 'GET',
+        headers: {
+          'X-Agent-ID': this.config.agentId,
+          'X-Claw-Identifier': this.config.clawIdentifier,
+        },
+      });
+      return response?.slots ?? null;
+    } catch {
+      return null;
+    }
+  }
+
   // -------------------------------------------------------------------------
   // Internal helpers
   // -------------------------------------------------------------------------