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

packages/shared/src/schemas/payments.ts

@@ -0,0 +1,35 @@
+import { z } from 'zod';
+import { createPageSchema, createPageSizeSchema, createPaginationSchema } from './pagination.js';
+
+const isoDateTimeSchema = z.string().datetime();
+const pageSchema = createPageSchema();
+const pageSizeSchema = createPageSizeSchema(10);
+const paginationSchema = createPaginationSchema();
+
+export const paymentStatusSchema = z.enum(['PENDING', 'PAID', 'OVERDUE', 'CANCELLED']);
+
+export const PaymentDtoSchema = z.object({
+  id: z.string(),
+  groupId: z.string(),
+  studentId: z.string(),
+  amount: z.coerce.number().positive(),
+  currency: z.string(),
+  status: paymentStatusSchema,
+  dueDate: isoDateTimeSchema,
+  paidAt: isoDateTimeSchema.nullable(),
+  createdAt: isoDateTimeSchema,
+  updatedAt: isoDateTimeSchema,
+});
+export type PaymentDto = z.output<typeof PaymentDtoSchema>;
+
+export const PaymentQuerySchema = z.object({
+  page: pageSchema,
+  pageSize: pageSizeSchema,
+});
+export type PaymentQuery = z.output<typeof PaymentQuerySchema>;
+
+export const PaymentListSchema = z.object({
+  data: z.array(PaymentDtoSchema),
+  pagination: paginationSchema,
+});
+export type PaymentList = z.output<typeof PaymentListSchema>;