fix: recurring event display and AI query improvements

- Use occurrenceStart instead of startTime in getEventsInRange so
  recurring events show their actual occurrence date to the AI
- Add lazy CalDAV sync in ChatService (syncOnce before first DB access)
- Add CaldavService.sync() with internal config check (silent no-op)
- Show German recurrence description (e.g. "Jede Woche") instead of
  generic "Wiederkehrend" in EventCardBase via formatRecurrenceRule()
- Move RepeatType and REPEAT_TYPE_LABELS from editEvent to shared
- Separate calendar overlay useFocusEffect from event loading

apps/client/src/app/(tabs)/calendar.tsx

@@ -122,17 +122,22 @@ const Calendar = () => {
   // Load events when tab gains focus or month/year changes
   // NOTE: Wrapper needed because loadEvents is async (returns Promise)
   // and useFocusEffect expects a sync function (optionally returning cleanup)
-  // Also re-open overlay if selectedDate exists (for back navigation from editEvent)
   useFocusEffect(
     useCallback(() => {
       loadEvents();
-      if (selectedDate) {
-        setOverlayVisible(true);
-      }
 
       const interval = setInterval(loadEvents, 10_000);
       return () => clearInterval(interval);
-    }, [loadEvents, selectedDate]),
+    }, [loadEvents]),
+  );
+
+  // Re-open overlay after back navigation from editEvent
+  useFocusEffect(
+    useCallback(() => {
+      if (selectedDate) {
+        setOverlayVisible(true);
+      }
+    }, [selectedDate]),
   );
 
   // Group events by date (YYYY-MM-DD format)

apps/client/src/app/editEvent.tsx

@@ -19,7 +19,7 @@ import { Ionicons } from "@expo/vector-icons";
 import { ScrollableDropdown } from "../components/ScrollableDropdown";
 import { useDropdownPosition } from "../hooks/useDropdownPosition";
 import { EventService, ChatService } from "../services";
-import { buildRRule, CreateEventDTO } from "@calchat/shared";
+import { buildRRule, CreateEventDTO, REPEAT_TYPE_LABELS, RepeatType } from "@calchat/shared";
 import { useChatStore } from "../stores";
 import CustomTextInput, {
   CustomTextInputProps,
@@ -86,15 +86,6 @@ const PickerRow = ({
   );
 };
 
-type RepeatType = "Tag" | "Woche" | "Monat" | "Jahr";
-
-const REPEAT_TYPE_LABELS: Record<RepeatType, string> = {
-  Tag: "Tage",
-  Woche: "Wochen",
-  Monat: "Monate",
-  Jahr: "Jahre",
-};
-
 type RepeatPressableProps = {
   focused: boolean;
   repeatType: RepeatType;