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;

apps/client/src/components/EventCard.tsx

@@ -19,7 +19,7 @@ export const EventCard = ({ event, onEdit, onDelete }: EventCardProps) => {
         startTime={event.occurrenceStart}
         endTime={event.occurrenceEnd}
         description={event.description}
-        isRecurring={!!event.recurrenceRule}
+        recurrenceRule={event.recurrenceRule}
       >
         {/* Action buttons - TouchableOpacity with delayPressIn allows ScrollView to detect scroll gestures */}
         <View className="flex-row justify-end mt-3 gap-3">

apps/client/src/components/EventCardBase.tsx

@@ -8,6 +8,7 @@ import {
   formatDateWithWeekday,
   formatDateWithWeekdayShort,
   formatTime,
+  formatRecurrenceRule,
 } from "@calchat/shared";
 
 type EventCardBaseProps = {
@@ -16,7 +17,7 @@ type EventCardBaseProps = {
   startTime: Date;
   endTime: Date;
   description?: string;
-  isRecurring?: boolean;
+  recurrenceRule?: string;
   children?: ReactNode;
 };
 
@@ -46,7 +47,7 @@ export const EventCardBase = ({
   startTime,
   endTime,
   description,
-  isRecurring,
+  recurrenceRule,
   children,
 }: EventCardBaseProps) => {
   const { theme } = useThemeStore();
@@ -95,7 +96,7 @@ export const EventCardBase = ({
       </View>
 
       {/* Recurring indicator */}
-      {isRecurring && (
+      {recurrenceRule && (
         <View className="flex-row items-center mb-1">
           <Feather
             name="repeat"
@@ -103,7 +104,9 @@ export const EventCardBase = ({
             color={theme.textPrimary}
             style={{ marginRight: 8 }}
           />
-          <Text style={{ color: theme.textPrimary }}>Wiederkehrend</Text>
+          <Text style={{ color: theme.textPrimary }}>
+            {formatRecurrenceRule(recurrenceRule)}
+          </Text>
         </View>
       )}
 

apps/client/src/components/ProposedEventCard.tsx

@@ -113,7 +113,7 @@ export const ProposedEventCard = ({
         startTime={event.startTime}
         endTime={event.endTime}
         description={event.description}
-        isRecurring={!!event.recurrenceRule}
+        recurrenceRule={event.recurrenceRule}
       >
         {/* Show new exception date for delete/single actions */}
         {newExceptionDate && (