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/src/modules/groups/lib/helpers.ts

@@ -0,0 +1,33 @@
+import type { PrismaClient } from '@generated/prisma/client';
+import type { GroupDto } from '@gruperly/shared';
+
+export type GroupDb = Pick<PrismaClient, 'group' | 'groupMember' | 'organization'>;
+
+type GroupRecord = {
+  id: string;
+  name: string;
+  description: string | null;
+  createdById: string;
+  createdAt: Date;
+  updatedAt: Date;
+};
+
+export function toGroupDto(record: GroupRecord): GroupDto {
+  return {
+    id: record.id,
+    name: record.name,
+    description: record.description,
+    createdById: record.createdById,
+    createdAt: record.createdAt.toISOString(),
+    updatedAt: record.updatedAt.toISOString(),
+  };
+}
+
+export function buildGroupWhereForUser(userId: string) {
+  return {
+    OR: [
+      { createdById: userId },
+      { members: { some: { userId } } },
+    ],
+  };
+}