fix: resolve all failing tests and type errors

[stooit]

Summary

Fixes all 22 failing tests and eliminates all TypeScript type errors across both packages.

Changes

• Pagination utility (packages/shared/src/utils/pagination.ts): Implemented the paginate() function that was previously a stub throwing "not implemented". Correctly slices items by page/size and returns PaginatedResponse<T> with total, totalPages, and page metadata.

• User type field name (packages/shared/src/types.ts): Renamed userName → username to match the field name used in route handlers and tests.

• Auth middleware case-sensitivity (packages/api/src/middleware/auth.ts): Fixed HTTP method comparison to be case-insensitive, so public routes like POST /users are correctly excluded from auth checks.

• Missing import (packages/api/src/routes/users.ts): Added missing badRequest import from the response helpers module.

• TypeScript config (tsconfig.json): Added bun-types to compiler options for proper Bun global type resolution.

Verification

bun test → 22 pass, 0 fail, 37 expect() calls
npx tsc --noEmit → no errors

Assumptions

• No test files were modified
• No new dependencies were added
• The bun-types package was already available in node_modules