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

turbo.json

@@ -10,10 +10,13 @@
       "persistent": true
     },
     "lint": {
-      "dependsOn": ["^lint"]
+      "dependsOn": ["^build"]
+    },
+    "lint:fix": {
+      "dependsOn": ["^build"]
     },
     "typecheck": {
       "dependsOn": ["^typecheck"]
     }
   }
-}
+}