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/package.json

@@ -6,17 +6,19 @@
   "main": "./src/index.ts",
   "types": "./src/index.ts",
   "exports": {
-    ".": "./src/index.ts",
-    "./schemas/*": "./src/schemas/*"
+    ".": "./src/index.ts"
   },
   "scripts": {
-    "typecheck": "tsc --noEmit"
+    "typecheck": "tsc --noEmit",
+    "lint": "biome check .",
+    "lint:fix": "biome check . --write"
   },
   "dependencies": {
-    "zod": "^3.24.0"
+    "zod": "3.24.2"
   },
   "devDependencies": {
-    "@prisma/client": "^7.10.0",
+    "@biomejs/biome": "^2.4.15",
+    "@gruperly/config": "workspace:*",
     "typescript": "^5.7.0"
   }
-}
+}