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/prisma.config.ts

@@ -0,0 +1,15 @@
+import { join } from 'node:path'
+import { config } from 'dotenv'
+import { defineConfig, env } from 'prisma/config'
+
+config({ path: join(process.cwd(), '.env') })
+
+export default defineConfig({
+  schema: 'prisma/',
+  migrations: {
+    path: 'prisma/migrations',
+  },
+  datasource: {
+    url: env('DATABASE_URL'),
+  },
+})