V3-14: GPX <type> from activity (code only)

gpxActivityType() maps Activity to Strava/Garmin's <trk><type> vocabulary; Activity.other omits the element rather than writing it empty. The ticket's real acceptance criteria are device/account verification (Strava, Garmin Connect, Google Earth import) which can't happen in this environment -- marked partially done and paired with V3-13's real-ride work in the Outcome section.

test/ride_export_test.dart

@@ -141,6 +141,33 @@ void main() {
       expect(doc.findAllElements('trkpt').length, 1,
           reason: 'no point may be silently dropped');
     });
+
+    test('<type> reflects the trip activity (V3-14)', () {
+      final r = ride(segmentCount: 1, perSegment: 1);
+      final bike = trip.copyWith(activity: Activity.bicycle);
+
+      final doc = XmlDocument.parse(gpx(bike, r.segments, r.points, 'Ride'));
+
+      expect(doc.findAllElements('type').single.innerText, 'cycling');
+    });
+
+    test('<type> is absent, not empty, for Activity.other (V3-14)', () {
+      final r = ride(segmentCount: 1, perSegment: 1);
+      final other = trip.copyWith(activity: Activity.other);
+
+      final doc = XmlDocument.parse(gpx(other, r.segments, r.points, 'Ride'));
+
+      expect(doc.findAllElements('type'), isEmpty,
+          reason: 'an empty <type/> would falsely claim the element exists');
+    });
+
+    test('gpxActivityType covers every activity without throwing', () {
+      for (final activity in Activity.values) {
+        // Must not throw; only Activity.other is allowed to map to null.
+        final type = gpxActivityType(activity);
+        expect(type == null, activity == Activity.other);
+      }
+    });
   });
 
   group('geojson', () {