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

CLAUDE.md

@@ -334,7 +334,7 @@ src/
     ├── index.ts
     ├── dateHelpers.ts    # getDay() - get date for specific weekday relative to today
     ├── formatters.ts     # formatDate(), formatTime(), formatDateTime(), formatDateWithWeekday() - German locale
-    └── rruleHelpers.ts   # parseRRule() - parse RRULE strings to extract freq, until, count, interval, byDay
+    └── rruleHelpers.ts   # parseRRule(), buildRRule(), formatRecurrenceRule() - RRULE parsing, building, and German formatting
 ```
 
 **Key Types:**
@@ -408,6 +408,10 @@ CalDAV sync with external calendar servers (e.g., Radicale) using `tsdav` and `i
 - **Calendar timer** (`calendar.tsx`): Every 10s while Calendar tab is focused, via `setInterval` in `useFocusEffect`
 - **Sync button** (`settings.tsx`): Manual trigger in CaldavSettings
 
+**Lazy sync (server-side in ChatService):**
+- AI data access callbacks (`fetchEventsInRange`, `searchEvents`, `fetchEventById`) trigger `syncOnce()` before the first DB query
+- Uses `CaldavService.sync()` which checks config internally (silent no-op without config)
+
 **Single-event sync (server-side in controllers):**
 - `EventController`: `pushToCaldav()` after create/update, `deleteFromCaldav()` after delete
 - `ChatController`: `pushAll()` after confirming an event proposal
@@ -419,7 +423,7 @@ CalDAV sync with external calendar servers (e.g., Radicale) using `tsdav` and `i
 
 **Architecture:**
 - `CaldavService` depends on `CaldavRepository` (config storage) and `EventService` (event CRUD)
-- `ChatService` depends only on `EventService` (not EventRepository) for all event operations
+- `ChatService` depends on `EventService` and `CaldavService` (lazy CalDAV sync on AI data access)
 - `EventController` and `ChatController` both receive `CaldavService` for CalDAV push on mutations
 
 ### Database Abstraction
@@ -568,12 +572,12 @@ NODE_ENV=development        # development = pretty logs, production = JSON
   - `utils/recurrenceExpander`: Handles RRULE parsing, strips `RRULE:` prefix if present (AI may include it), filters out exceptionDates
   - `logging/`: Structured logging with pino, pino-http middleware, @Logged decorator
   - All repositories and GPTAdapter decorated with @Logged for automatic method logging
-  - `CaldavService`: Full CalDAV sync (connect, pullEvents, pushEvent, pushAll, deleteEvent, getConfig, saveConfig, deleteConfig)
+  - `CaldavService`: Full CalDAV sync (connect, pullEvents, pushEvent, pushAll, deleteEvent, sync, getConfig, saveConfig, deleteConfig). `sync()` checks config internally and is a silent no-op without config.
   - `CaldavController`: REST endpoints for config CRUD, pull, push
   - `MongoCaldavRepository`: Config persistence with createOrUpdate, findByUserId, deleteByUserId
   - `EventController`: CalDAV push on create/update, CalDAV delete on delete (via pushToCaldav/deleteFromCaldav helpers)
   - `ChatController`: CalDAV pushAll after confirmEvent (ensures chat-created events sync)
-  - `ChatService`: Refactored to use only EventService (no direct EventRepository dependency)
+  - `ChatService`: Uses EventService + CaldavService (lazy sync on AI data access via syncOnce pattern)
   - `EventService`: Extended with searchByTitle(), findByCaldavUUID()
   - `utils/eventFormatters`: Refactored to use EventService instead of EventRepository
   - CORS configured to allow X-User-Id header
@@ -584,7 +588,7 @@ NODE_ENV=development        # development = pretty logs, production = JSON
 
 **Shared:**
 - Types, DTOs, constants (Day, Month with German translations), ExpandedEvent type, CaldavConfig, CaldavSyncStatus defined and exported
-- `rruleHelpers.ts`: `parseRRule()` parses RRULE strings using rrule library, returns `ParsedRRule` with freq, until, count, interval, byDay
+- `rruleHelpers.ts`: `parseRRule()` parses RRULE strings using rrule library, returns `ParsedRRule` with freq, until, count, interval, byDay. `buildRRule()` builds RRULE from RepeatType + interval. `formatRecurrenceRule()` formats RRULE into German description (e.g., "Jede Woche", "Alle 2 Monate"). Exports `REPEAT_TYPE_LABELS` and `RepeatType`.
 - `formatters.ts`: German date/time formatters (`formatDate`, `formatTime`, `formatDateTime`, `formatDateWithWeekday`, `formatDateKey`) used by both client and server
 - rrule library added as dependency for RRULE parsing
 
@@ -634,7 +638,7 @@ NODE_ENV=development        # development = pretty logs, production = JSON
 - `CustomTextInput`: Themed text input component with focus border highlight, supports controlled value via `text` prop
 - `CardBase`: Reusable card component with header (title/subtitle), content area, and optional footer button - configurable padding, border, text size via props, ScrollView uses `nestedScrollEnabled` for Android
 - `ModalBase`: Reusable modal wrapper with backdrop (absolute-positioned behind card), uses CardBase internally - provides click-outside-to-close, Android back button support, and proper scrolling on Android
-- `EventCardBase`: Event card with date/time/recurring icons - uses CardBase for structure
+- `EventCardBase`: Event card with date/time/recurring icons - uses CardBase for structure. Accepts `recurrenceRule` string (not boolean) and displays German-formatted recurrence via `formatRecurrenceRule()`
 - `EventCard`: Uses EventCardBase + edit/delete buttons (TouchableOpacity with delayPressIn for scroll-friendly touch handling)
 - `ProposedEventCard`: Uses EventCardBase + confirm/reject/edit buttons for chat proposals, displays green highlighted text for new changes ("Neue Ausnahme: [date]" for single delete, "Neues Ende: [date]" for UNTIL updates), shows yellow conflict warnings when proposed time overlaps with existing events. Edit button allows modifying proposals before confirming.
 - `DeleteEventModal`: Delete confirmation modal using ModalBase - shows three options for recurring events (single/future/all), simple confirm for non-recurring