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/src/lib/result.ts

@@ -0,0 +1,13 @@
+export type Result<TValue, TError> =
+  | { ok: true; value: TValue }
+  | { ok: false; error: TError };
+
+export const ok = <TValue>(value: TValue): Result<TValue, never> => ({
+  ok: true,
+  value,
+});
+
+export const err = <TError>(error: TError): Result<never, TError> => ({
+  ok: false,
+  error,
+});