fix: resolve failing tests and type errors across api and shared packages

[stooit]

Summary

Fixes all failing tests and type errors. bun test → 22 pass / 0 fail; bunx tsc --noEmit → clean (exit 0).

Changes

• Auth middleware (packages/api/src/middleware/auth.ts): corrected HTTP-method case comparison so POST /users is correctly treated as a public route (case-sensitivity bug).
• Users route (packages/api/src/routes/users.ts): imported the missing badRequest helper (was throwing ReferenceError); aligned field usage to the shared User type; removed a stale BUG comment.
• Shared types (packages/shared/src/types.ts): fixed inconsistent User field name so the API package and tests agree.
• Pagination (packages/shared/src/utils/pagination.ts): implemented paginate() (previously a stub that threw not implemented) — handles page slicing, partial last page, out-of-range pages, empty input, and totalPages rounding.
• tsconfig (tsconfig.json): added "types": ["bun-types"] so tsc resolves process and bun:test globals.

Verification

• bun test: 22 passed, 0 failed, 37 assertions
• bunx tsc --noEmit: no errors

Notes / Assumptions

• No test files were modified; no new dependencies added (bun-types already present in node_modules).
• Reviewed for correctness (auth method handling, field-name consistency, pagination edge cases) — clean.