fix: resolve failing tests and type errors

[stooit]

Summary

• shared/pagination: implemented paginate (slice by page/size, totalPages = ceil(total/size), empty for out-of-range pages, guards size<=0).
• shared/types: renamed User.userName → username to match api routes and tests.
• api/routes/users: added missing badRequest import (was a runtime ReferenceError on invalid POST).
• api/middleware/auth: fixed method case-sensitivity bug ("post" vs "POST"); public methods now compared via uppercase Set.
• tsconfig: added "types": ["bun-types"] (already a devDependency) so bun:test and process resolve.

Verification

bun test → 22 pass / 0 fail; tsc --noEmit → clean.

Assumptions

• Unauthenticated POST /users is intended behaviour, as asserted by auth.test.ts.
• @types/node resolves transitively via bun-types; no new dependencies added. No test files modified.