feat: section 4 — Android battery optimization prompt

One-time prompt on first launch (Android only) directing the user to
exclude bincio-rec from battery optimization. Uses the direct
REQUEST_IGNORE_BATTERY_OPTIMIZATIONS system dialog with a fallback to
the general settings page for OEMs that block the direct intent.
Dismissal persisted in AsyncStorage so prompt never repeats.

CLAUDE.md

@@ -117,9 +117,9 @@ Items below are what remains before v1 is shippable.
 - [x] **Permission request** — `requestNotificationPermissions()` called in `App.tsx` on mount; foreground notification handler set at module level so iOS shows banners while app is active
 - [x] **Milestone tracker** — module-level `runningDistanceMeters` / `lastNotifiedKm` / `prevPoint` in `gps.ts`, reset on each `startGpsRecording()`; each incoming location adds haversine distance and fires a notification when a new km is crossed, gated on the `kmNotifications` AsyncStorage setting
 
-### 4 — Android battery optimization prompt (1–2 hours)
+### 4 — Android battery optimization prompt ✅
 
-- [ ] On first launch, detect if the app is affected by battery optimization (`expo-intent-launcher`) and show a one-time prompt directing the user to whitelist bincio-rec; persist dismissal in AsyncStorage so it only shows once
+- [x] `src/services/batteryOptimization.ts` — Android-only, one-time prompt (dismissed flag in AsyncStorage); uses `REQUEST_IGNORE_BATTERY_OPTIMIZATIONS` intent to open the system dialog for bincio-rec directly; falls back to `IGNORE_BATTERY_OPTIMIZATION_SETTINGS` (general page) on OEMs that block the direct intent; called from `App.tsx` on mount alongside notification permission request
 
 ### 5 — Map (optional upgrade)