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/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 && (