refactor: migrate backend to pnpm monorepo with Hono module architecture

- Replace Bun with pnpm 9 + Turborepo + tsx; apps/api renamed to apps/backend
- Split backend into http/, modules/, lib/ layers mirroring tai-specguard
- Add use-case + Result pattern, Problem Details RFC 7807, basePath /api/v1
- Mount Better Auth at /api/v1/auth, keep session-auth whitelist
- Split Prisma schema into prisma/models/*, generate into generated/
- Rework packages/shared into lib/ + schemas/ with pagination DTOs
- Implement health, groups, students, payments, waitlist modules
- Add vitest suite with prisma mocks (21 tests), biome lint
- Point web client to /api/v1/auth and /api/v1/groups/from-organization

apps/backend/test/students.test.ts

@@ -0,0 +1,83 @@
+import { Hono } from 'hono';
+import { beforeEach, describe, expect, it, vi } from 'vitest';
+
+vi.mock('@/lib/prisma', () => ({
+  default: {
+    student: {
+      findMany: vi.fn(),
+      count: vi.fn(),
+    },
+  },
+  getPrismaClient: vi.fn(),
+  UnitOfWork: class {},
+}));
+
+import prisma from '@/lib/prisma';
+import { studentsRoutes } from '@/modules/students';
+
+const app = new Hono();
+app.route('/students', studentsRoutes);
+
+const student = {
+  id: 'student-1',
+  groupId: 'group-1',
+  fullName: 'Ana Pérez',
+  email: 'ana@example.com',
+  phone: null,
+  guardianName: 'Luis Pérez',
+  guardianPhone: null,
+  notes: null,
+  createdAt: new Date('2026-08-01T10:00:00.000Z'),
+  updatedAt: new Date('2026-08-01T10:00:00.000Z'),
+};
+
+describe('students routes', () => {
+  beforeEach(() => {
+    vi.clearAllMocks();
+  });
+
+  it('lists students with pagination', async () => {
+    vi.mocked(prisma.student.findMany).mockResolvedValue([student]);
+    vi.mocked(prisma.student.count).mockResolvedValue(21);
+
+    const res = await app.request('/students?page=2&pageSize=10');
+
+    expect(res.status).toBe(200);
+    expect(await res.json()).toEqual({
+      data: [
+        {
+          ...student,
+          createdAt: student.createdAt.toISOString(),
+          updatedAt: student.updatedAt.toISOString(),
+        },
+      ],
+      pagination: { page: 2, pageSize: 10, total: 21, totalPages: 3 },
+    });
+    expect(prisma.student.findMany).toHaveBeenCalledWith({
+      skip: 10,
+      take: 10,
+      orderBy: { createdAt: 'desc' },
+    });
+    expect(prisma.student.count).toHaveBeenCalledWith();
+  });
+
+  it('uses default pagination', async () => {
+    vi.mocked(prisma.student.findMany).mockResolvedValue([]);
+    vi.mocked(prisma.student.count).mockResolvedValue(0);
+
+    const res = await app.request('/students');
+
+    expect(res.status).toBe(200);
+    expect(await res.json()).toEqual({
+      data: [],
+      pagination: { page: 1, pageSize: 10, total: 0, totalPages: 0 },
+    });
+  });
+
+  it('rejects invalid pagination query parameters', async () => {
+    const res = await app.request('/students?page=0&pageSize=25');
+
+    expect(res.status).toBe(400);
+    expect(await res.json()).toMatchObject({ status: 400, title: 'Bad Request' });
+  });
+});