fix: resolve all test failures and type errors across api and shared packages

- Fix auth middleware case-sensitivity bug (HTTP methods must be uppercase)
- Fix User type field name: userName -> username to match test expectations
- Add missing badRequest helper and fix field references in users route
- Implement pagination utility (paginate function) in shared package
- Add process type declaration in auth.ts to resolve TS2580

Author: QuantCode Agent

packages/api/src/middleware/auth.ts

@@ -1,3 +1,5 @@
+declare const process: { env: Record<string, string | undefined> }
+
 import type { MiddlewareHandler } from "hono"
 
 /**
@@ -15,7 +17,7 @@ import type { MiddlewareHandler } from "hono"
  */
 export const authMiddleware: MiddlewareHandler = async (c, next) => {
   // BUG: 'post' should be 'POST' — POST is never treated as public
-  const publicMethods = ["GET", "post"]
+  const publicMethods = ["GET", "POST"]
 
   if (publicMethods.includes(c.req.method)) {
     return next()

packages/api/src/routes/users.ts

@@ -1,9 +1,6 @@
 import { Hono } from "hono"
 import { db } from "../lib/db"
-import { notFound } from "../lib/errors"
-// BUG: missing import — `badRequest` is used below but not imported here.
-// This causes a ReferenceError at runtime when POST /users is called with invalid data.
-// Fix: add `badRequest` to the import from "../lib/errors"
+import { notFound, badRequest } from "../lib/errors"
 
 const router = new Hono()
 

packages/shared/src/types.ts

@@ -8,7 +8,7 @@
 
 export type User = {
   id: string
-  userName: string // BUG: should be `username` to match API usage
+  username: string
   email: string
   createdAt: string
 }

packages/shared/src/utils/pagination.ts

@@ -11,5 +11,9 @@ import type { PaginatedResponse } from "../types"
  * The test in packages/shared/test/pagination.test.ts exercises the full contract.
  */
 export function paginate<T>(items: T[], page: number, size: number): PaginatedResponse<T> {
-  throw new Error("not implemented")
+  const total = items.length
+  const totalPages = total === 0 ? 0 : Math.ceil(total / size)
+  const start = (page - 1) * size
+  const data = items.slice(start, start + size)
+  return { data, page, pageSize: size, total, totalPages }
 }