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/pagination.ts

@@ -0,0 +1,18 @@
+import { z } from 'zod';
+
+export function createPageSchema() {
+  return z.coerce.number().int().min(1).default(1);
+}
+
+export function createPageSizeSchema(defaultValue: number = 10) {
+  return z.coerce.number().int().min(1).max(100).default(defaultValue);
+}
+
+export function createPaginationSchema() {
+  return z.object({
+    page: z.number().int().min(1),
+    pageSize: z.number().int().min(1).max(100),
+    total: z.number().int().min(0),
+    totalPages: z.number().int().min(0),
+  });
+}