feat: replace Claude with GPT for AI chat integration

- Replace ClaudeAdapter with GPTAdapter using OpenAI GPT (gpt-5-mini)
- Implement function calling for calendar operations (getDay, proposeCreate/Update/Delete, searchEvents)
- Add provider-agnostic AI utilities in ai/utils/ (systemPrompt, toolDefinitions, toolExecutor, eventFormatter)
- Add USE_TEST_RESPONSES env var to toggle between real AI and test responses
- Switch ChatService.processMessage to use real AI provider
- Add npm run format command for Prettier
- Update CLAUDE.md with new architecture

apps/server/src/ai/utils/eventFormatter.ts

@@ -0,0 +1,29 @@
+import { CalendarEvent } from "@caldav/shared";
+
+// German date/time formatting helpers
+export const formatDate = (d: Date) => d.toLocaleDateString("de-DE");
+export const formatTime = (d: Date) =>
+  d.toLocaleTimeString("de-DE", { hour: "2-digit", minute: "2-digit" });
+export const formatDateTime = (d: Date) =>
+  `${formatDate(d)} ${d.toLocaleTimeString("de-DE")}`;
+
+/**
+ * Format a list of events for display in the system prompt.
+ * Output is in German with date/time formatting.
+ */
+export function formatExistingEvents(events: CalendarEvent[]): string {
+  if (events.length === 0) {
+    return "Keine Termine vorhanden.";
+  }
+
+  return events
+    .map((e) => {
+      const start = new Date(e.startTime);
+      const end = new Date(e.endTime);
+      const timeStr = `${formatTime(start)} - ${formatTime(end)}`;
+      const recurring = e.isRecurring ? " (wiederkehrend)" : "";
+      const desc = e.description ? ` | ${e.description}` : "";
+      return `- ${e.title} (ID: ${e.id}) | ${formatDate(start)} ${timeStr}${recurring}${desc}`;
+    })
+    .join("\n");
+}