feat: add pagination to search results

[KKamJi98]

Type of change

• New feature (non-breaking change which adds functionality)

Description

• mirror the home page paginator UI in the search panel so users can browse search results page by page
• cache raw SimpleJekyllSearch output and render only the active page, keeping the DOM small and the behavior consistent on desktop/mobile (including ellipsis + prev/next arrows)
• expose search.limit and search.per_page in _config.yml so site owners can control how many hits are fetched and shown per page
• added regression coverage by running bash tools/test.sh

Additional context

• Fixes Make search result limit configurable #2583