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/tsconfig.json

@@ -0,0 +1,17 @@
+{
+  "extends": "@gruperly/config/tsconfig.base.json",
+  "compilerOptions": {
+    "moduleResolution": "bundler",
+    "types": ["node"],
+    "declaration": false,
+    "noEmit": false,
+    "outDir": "./dist",
+    "rootDir": ".",
+    "paths": {
+      "@/*": ["./src/*"],
+      "@generated/*": ["./generated/*"]
+    }
+  },
+  "include": ["src/**/*.ts", "generated/prisma/**/*.ts"],
+  "exclude": ["node_modules", "dist", "test"]
+}