Setup initial project

packages/api/src/schemas/household.schema.test.ts

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+import { describe, it, expect } from 'vitest';
+import { HouseholdModel } from './household.schema.js';
+
+describe('HouseholdModel', () => {
+  it('is a valid mongoose model', () => {
+    expect(HouseholdModel.modelName).toBe('Household');
+  });
+
+  it('has expected schema paths', () => {
+    const paths = Object.keys(HouseholdModel.schema.paths);
+    expect(paths).toContain('name');
+    expect(paths).toContain('ownerUserId');
+    expect(paths).toContain('members');
+    expect(paths).toContain('inviteCode');
+    expect(paths).toContain('settings');
+    expect(paths).toContain('createdAt');
+    expect(paths).toContain('updatedAt');
+  });
+});