perf(mobile): seed nav with last-known fix on Start ride

Tapping Start ride used to wait for the first live GPS tick before
NavigationState emitted, which can take several seconds after a cold
start. Fetch the cached last-known position (no GPS wait) and feed it
into the Ferrostar controller before the live stream attaches, so the
ETA sheet populates immediately and the live stream just keeps it
fresh.

Author: cafca

mobile/lib/navigation/navigation_service.dart

@@ -50,6 +50,7 @@ class NavigationService {
   Future<void> start({
     required WaypointInput origin,
     required WaypointInput destination,
+    UserLocation? initialLocation,
   }) async {
     await dispose();
     _destination = destination;
@@ -60,6 +61,14 @@ class NavigationService {
     final waypoints = [origin, destination];
     _controller = await createController(routeJson, waypoints);
 
+    // Seed the controller with the last-known position before the live GPS
+    // stream attaches, so NavigationState emits immediately instead of
+    // waiting for the first fresh fix (which can take several seconds after
+    // a cold start).
+    if (initialLocation != null) {
+      await _controller!.updateLocation(initialLocation);
+    }
+
     _stateSub = _controller!.stateStream.listen(
       _stateController.add,
       onError: _stateController.addError,

mobile/lib/screens/map_screen.dart

@@ -17,6 +17,7 @@ import '../models/location.dart';
 import '../models/route_preview.dart';
 import '../models/route_state.dart';
 import '../navigation/camera_controller.dart';
+import '../navigation/location_converter.dart';
 import '../navigation/maneuver_icons.dart';
 import '../navigation/nav_constants.dart';
 import '../providers/navigation_camera_provider.dart';
@@ -270,11 +271,19 @@ class _MapScreenState extends ConsumerState<MapScreen> {
     }
     debugPrint('nav: start ${origin.name} -> ${destination.name}');
     final service = ref.read(navigationServiceProvider);
+    // Fetch last-known position synchronously (no GPS wait) so the controller
+    // has an initial fix and NavigationState emits immediately.
+    UserLocation? initial;
+    try {
+      final pos = await Geolocator.getLastKnownPosition();
+      if (pos != null) initial = positionToUserLocation(pos);
+    } catch (_) {}
     try {
       await service.start(
         origin: WaypointInput(lat: origin.lat, lng: origin.lng),
         destination:
             WaypointInput(lat: destination.lat, lng: destination.lng),
+        initialLocation: initial,
       );
     } catch (e, st) {
       debugPrint('nav: start failed: $e\n$st');