Summary

Fixes all failing tests and TypeScript errors across the api and shared packages. Final state: bun test → 22 pass / 0 fail; bunx tsc --noEmit → exit 0.

Changes

• shared/types: renamed User.userName → username to align the shared type with its consumers and the test contract (was causing tsc errors in routes/users.ts and the users tests).
• shared/pagination: implemented the paginate() stub (previously threw not implemented) — 1-based paging with slice-based windowing, correct total/totalPages, and empty data for out-of-range pages.
• api/auth middleware: fixed HTTP method case in the public-route allow-list (post → POST) so POST /users is correctly treated as public (no token required).
• api/routes/users: added the missing badRequest import so 400 responses for missing fields resolve at runtime.
• tsconfig: added bun-types to compilerOptions.types to resolve the bun:test module and process globals (uses an already-present dependency; no new deps added).

Verification

bun test          → 22 pass, 0 fail, 37 expect() calls
bunx tsc --noEmit → exit 0

Assumptions

• Field name: tests and route consumers expect username, so the shared type was changed to match (rather than editing tests).
• Pagination is 1-based, matching the test expectations.
• The bun:test/process tsc errors were a tsconfig wiring gap (missing bun-types in types), not a missing dependency — resolved via config only.

Constraints honoured

• No test files modified.
• No new dependencies added.
• Only source needed to satisfy the tests was changed.