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/schedule-cache.ts

@@ -0,0 +1,109 @@
+/**
+ * Local cache of today's calendar schedule.
+ * Synced periodically from HF backend, checked locally for due slots.
+ */
+
+import type { CalendarSlotResponse } from "./types.js";
+
+export class ScheduleCache {
+  private slots: Map<string, CalendarSlotResponse> = new Map();
+  private lastSyncAt: Date | null = null;
+  private cachedDate: string | null = null; // YYYY-MM-DD
+
+  /**
+   * Replace the cache with a fresh schedule from backend.
+   */
+  sync(date: string, slots: CalendarSlotResponse[]): void {
+    // If date changed, clear old data
+    if (this.cachedDate !== date) {
+      this.slots.clear();
+    }
+    this.cachedDate = date;
+
+    // Merge: update existing slots, add new ones
+    const incomingIds = new Set<string>();
+    for (const slot of slots) {
+      const id = this.getSlotId(slot);
+      incomingIds.add(id);
+      this.slots.set(id, slot);
+    }
+
+    // Remove slots that no longer exist on backend (cancelled etc.)
+    for (const id of this.slots.keys()) {
+      if (!incomingIds.has(id)) {
+        this.slots.delete(id);
+      }
+    }
+
+    this.lastSyncAt = new Date();
+  }
+
+  /**
+   * Get slots that are due (scheduled_at <= now) and still pending.
+   */
+  getDueSlots(now: Date): CalendarSlotResponse[] {
+    const results: CalendarSlotResponse[] = [];
+    for (const slot of this.slots.values()) {
+      if (slot.status !== "not_started" && slot.status !== "deferred") continue;
+      if (!slot.scheduled_at) continue;
+
+      const scheduledAt = this.parseScheduledTime(slot.scheduled_at);
+      if (scheduledAt && scheduledAt <= now) {
+        results.push(slot);
+      }
+    }
+    // Sort by priority descending
+    results.sort((a, b) => (b.priority ?? 0) - (a.priority ?? 0));
+    return results;
+  }
+
+  /**
+   * Update a slot locally (e.g., after status change).
+   */
+  updateSlot(slotId: string, update: Partial<CalendarSlotResponse>): void {
+    const existing = this.slots.get(slotId);
+    if (existing) {
+      this.slots.set(slotId, { ...existing, ...update });
+    }
+  }
+
+  /**
+   * Remove a slot from cache.
+   */
+  removeSlot(slotId: string): void {
+    this.slots.delete(slotId);
+  }
+
+  /**
+   * Get all cached slots.
+   */
+  getAll(): CalendarSlotResponse[] {
+    return Array.from(this.slots.values());
+  }
+
+  /**
+   * Get cache metadata.
+   */
+  getStatus(): { slotCount: number; lastSyncAt: string | null; cachedDate: string | null } {
+    return {
+      slotCount: this.slots.size,
+      lastSyncAt: this.lastSyncAt?.toISOString() ?? null,
+      cachedDate: this.cachedDate,
+    };
+  }
+
+  private getSlotId(slot: CalendarSlotResponse): string {
+    return slot.virtual_id ?? String(slot.id);
+  }
+
+  private parseScheduledTime(scheduledAt: string): Date | null {
+    // scheduled_at can be "HH:MM:SS" (time only) or full ISO
+    if (/^\d{2}:\d{2}(:\d{2})?$/.test(scheduledAt)) {
+      // Time-only: combine with cached date
+      if (!this.cachedDate) return null;
+      return new Date(`${this.cachedDate}T${scheduledAt}Z`);
+    }
+    const d = new Date(scheduledAt);
+    return isNaN(d.getTime()) ? null : d;
+  }
+}