fix(search): validate pagination params strictly

[rissrice2105-agent]

Summary

• add a shared strict integer parser for API pagination params
• reject partial values like 10abc in public search/browse endpoints
• preserve existing status codes and validation messages for invalid pagination inputs

Tests

• pnpm exec vitest run src/lib/api/pagination.test.ts
• pnpm exec tsc --noEmit
• git diff --check

Notes

This is a small bug fix for the pinned repos Ugig flow. No invoice will be sent until the PR is merged/accepted.