Summary

Fixes all failing tests and TypeScript type errors in the multi-package Bun + Hono API repo. bun test now reports 22 pass / 0 fail and tsc --noEmit is clean.

Changes

• tsconfig.json — added "types": ["bun-types"] so tsc resolves bun:test and the process global (bun-types was already installed; no new dependency).
• packages/shared/src/types.ts — renamed User.userName → username to match the field name used by the route handlers and tests (cross-package field-name inconsistency).
• packages/shared/src/utils/pagination.ts — implemented the paginate() stub: page slicing, total, totalPages (0 for empty input), echoed page/pageSize, and safe empty/out-of-range handling.
• packages/api/src/middleware/auth.ts — fixed a case-sensitivity bug in the public-methods allow-list ("post" → "POST"); HTTP methods arrive uppercase, so POST /users was wrongly requiring a token. PUT/DELETE/PATCH still require a Bearer token (no security regression).
• packages/api/src/routes/users.ts — added the missing badRequest import from ../lib/errors (was a runtime ReferenceError).

Verification

• bun test → 22 pass, 0 fail (37 assertions)
• bunx tsc --noEmit → clean, zero errors
• No test files modified; no dependencies added.

Assumptions

• The username (lowercase) field name is canonical, since the tests and route handlers use it and tests must not change.
• Pagination requires no page clamping — Array.prototype.slice handles out-of-range pages gracefully and no test asserts clamping.