Summary

Fixes all failing tests and TypeScript errors in the multi-package repo. Baseline was 9 failing tests and 14 type errors; now 22 pass / 0 fail and tsc --noEmit is clean (exit 0).

Changes

• packages/shared/src/utils/pagination.ts — Implemented the paginate<T>() stub per the test contract: page slicing, total, totalPages (Math.ceil(total/pageSize), so 0 for empty), out-of-range pages return an empty slice, empty-array handling. Params clamped to a minimum of 1 and coerced against non-finite input.
• packages/shared/src/types.ts — Renamed User.userName → username to match the field name the tests assert.
• packages/api/src/routes/users.ts — Added the missing badRequest import (from ../lib/errors), fixing the POST /users 400-on-missing-fields path.
• packages/api/src/middleware/auth.ts — Fixed a case-sensitivity bug in the public-method allow-list. Now normalises the incoming method with toUpperCase() against a Set(["GET","POST"]), so GET/POST on /users are public regardless of casing and DELETE still 401s.
• tsconfig.json — Added "types": ["bun-types"] (already present in node_modules, no new dependency) to resolve Cannot find module 'bun:test' and Cannot find name 'process'.

Verification

bun test   -> 22 pass, 0 fail
tsc --noEmit -> exit 0

Constraints honoured

• No test files modified.
• No new dependencies added (bun-types was already installed).

Notes / assumptions

• Where a type and a test disagreed on a field name (userName vs username), the non-test source was changed to match the tests, per instructions.
• Security flag (out of scope, not changed): the auth policy leaves POST /users unauthenticated, which the tests deliberately require. This permits anonymous user-record creation and email collection — worth a security review before this pattern reaches production, but it was left as the tests mandate.