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/vitest.config.ts

@@ -0,0 +1,15 @@
+import path from 'node:path';
+import { defineConfig } from 'vitest/config';
+
+export default defineConfig({
+  test: {
+    globals: true,
+    environment: 'node',
+  },
+  resolve: {
+    alias: {
+      '@': path.resolve(__dirname, 'src'),
+      '@generated': path.resolve(__dirname, 'generated'),
+    },
+  },
+});