fix: resolve all failing tests and type errors

[stooit]

Summary

Fixes all failing tests and TypeScript type errors across the api and shared packages. Final state: 22 pass / 0 fail (bun test) and 0 type errors (tsc --noEmit).

Changes

• Pagination utility (packages/shared/src/utils/pagination.ts): implemented the previously-throwing stub — page slicing, total, totalPages, and page/pageSize fields with empty/out-of-range handling.
• Shared User type (packages/shared/src/types.ts + packages/api/src/routes/users.ts): renamed the field userName → username so the source matches what the tests expect (field-name inconsistency between packages).
• Missing import (packages/api/src/routes/users.ts): added the missing badRequest import that caused a failure.
• Auth middleware (packages/api/src/middleware/auth.ts): fixed an HTTP-method case-sensitivity bug so public routes (e.g. POST /users) are correctly matched.
• tsconfig (tsconfig.json): adjusted types so tsc resolves bun:test and process — no new dependencies added.

Verification

• bun test → 22 pass, 0 fail
• npx tsc --noEmit → exit 0

Notes / assumptions

• No test files were modified and no dependencies were added, per task constraints.
• Field name aligned to username (lowercase) because the test files reference that spelling; source was changed to match the tests.
• Reviewed by the review agent — fixes confirmed genuine (not test-passing hacks); only trivial stale-comment cleanups applied.