fix: Connect measurement unit preference to backend storage

Fixed measurement unit not persisting across page refreshes:

- Settings page now includes measurementUnit in the preferences object when saving
- MeasurementUnitSelector now accepts value/onChange props for controlled usage
- Settings state properly loads and saves measurementUnit from user preferences
- UnitInput component will now correctly read imperial/metric from user.preferences.measurementUnit

Previously, measurementUnit was only saved to localStorage but not synced to backend,
causing UnitInput to always default to metric since it reads from user.preferences.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

maternal-web/app/settings/page.tsx

@@ -28,6 +28,7 @@ export default function SettingsPage() {
     notifications: true,
     emailUpdates: false,
     darkMode: false,
+    measurementUnit: 'metric' as 'metric' | 'imperial',
   });
   const [isLoading, setIsLoading] = useState(false);
   const [error, setError] = useState<string | null>(null);
@@ -41,6 +42,7 @@ export default function SettingsPage() {
         notifications: user.preferences.notifications ?? true,
         emailUpdates: user.preferences.emailUpdates ?? false,
         darkMode: user.preferences.darkMode ?? false,
+        measurementUnit: (user.preferences.measurementUnit as 'metric' | 'imperial') || 'metric',
       });
       setTimeFormat(user.preferences.timeFormat || '12h');
     }
@@ -169,7 +171,10 @@ export default function SettingsPage() {
             <Box sx={{ display: 'flex', flexDirection: 'column', gap: 3, mt: 2 }}>
               <LanguageSelector />
               <Divider />
-              <MeasurementUnitSelector />
+              <MeasurementUnitSelector
+                value={settings.measurementUnit}
+                onChange={(value) => setSettings(prev => ({ ...prev, measurementUnit: value }))}
+              />
               <Divider />
               <TimeZoneSelector value={timezone} onChange={setTimezone} />
               <Divider />