fix: Handle family data correctly during registration and onboarding

- Extract family data from registration response and add to user object
- Backend returns family separately in registration, but included in user for login
- Remove error messages for language/measurement preferences (they save correctly)
- Add detailed console logging for debugging family issues
- Improve error message when family is missing during child creation

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

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

maternal-web/lib/auth/AuthContext.tsx

@@ -170,7 +170,7 @@ export const AuthProvider = ({ children }: { children: ReactNode }) => {
 
       // Backend returns { success, data: { user, family, tokens } }
       const { data: responseData } = response.data;
-      const { tokens, user: userData } = responseData;
+      const { tokens, user: userData, family: familyData } = responseData;
 
       if (!tokens?.accessToken || !tokens?.refreshToken) {
         throw new Error('Invalid response from server');
@@ -178,9 +178,19 @@ export const AuthProvider = ({ children }: { children: ReactNode }) => {
 
       const { accessToken, refreshToken } = tokens;
 
+      // Add family data to user object (registration returns family separately)
+      const userWithFamily = {
+        ...userData,
+        families: familyData ? [{
+          id: familyData.id,
+          familyId: familyData.id,
+          role: familyData.role || 'parent',
+        }] : [],
+      };
+
       tokenStorage.setTokens(accessToken, refreshToken);
       setToken(accessToken);
-      setUser(userData);
+      setUser(userWithFamily);
 
       // Redirect to onboarding
       router.push('/onboarding');