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

[stooit]

Summary

Fixes all failing tests and TypeScript type errors in the monorepo. Final state: 22 tests pass, 0 fail; tsc --noEmit clean (exit 0). No test files were modified; no dependencies added.

Changes

• Auth middleware (packages/api/src/middleware/auth.ts) — fixed an HTTP-method case-sensitivity bug: the public-method allow-list contained lowercase "post", so legitimate POST /users requests fell through to auth and returned 401. Now "POST".
• Users route (packages/api/src/routes/users.ts) — added the missing badRequest response-helper import that was causing a failure; aligned the create payload on the username field.
• Shared types (packages/shared/src/types.ts) — renamed the User field userName → username so the type matches what the tests (the source of truth) use. Removed a stale BUG: comment.
• Pagination utility (packages/shared/src/utils/pagination.ts) — implemented the previously-stubbed utility to satisfy its test.
• tsconfig.json — added bun-types to compilerOptions.types so process and bun:test resolve at type-check time without adding any dependency.

Verification

• bun test → 22 pass, 0 fail
• npx tsc --noEmit → no errors

Assumptions

• When a test and a type disagreed on a field name (username vs userName), the test was treated as authoritative since test files must not be modified — so the shared User type was changed to username.
• bun-types is already available in the workspace; it was added to tsconfig types rather than installed as a new dependency.