Add Search2 pagination and enable browse-all results for empty keyword

[ywkim312]

Closes: #230 #266

Description

Summary

• Add pagination to Search2 results with URL-synced state:
  • page and limit query params
  • page size selector
  • page navigation controls
  • correct offset-based fetching and result range display
• Keep pagination behavior consistent by resetting to page 1 when search inputs change:
  • keyword text
  • exact match toggle
  • resource type
  • active facet filters
  • page size
• Enable “browse-all” behavior for empty keyword searches:
  • when search text is empty, execute a no-keyword query
  • show initial/full results (subject to limit) instead of blank/no-results state
• Ensure initial route load executes once even when query state matches defaults, so empty-keyword landing is populated.

User-facing behavior changes

• Search2 now shows page navigation and X / page controls.
• URL reflects paging state and supports deep-linking/reload/back-forward for paged results.
• Opening Search2 with no keyword now shows results (browse mode), not an empty page.

Technical notes

• Pagination and URL sync logic is managed in FilterStateManager + useSearch.
• Result header now renders paging controls and range text (e.g., Showing 101-150 of N results).
• Empty-keyword execution is implemented as behavior gating only; no replacement of existing optimized query-building architecture.

Files changed

• client/src/services/FilterStateManager.js
• client/src/composables/useSearch.js
• client/src/components/facetsearch/ResultHeader2.vue
• client/src/components/facetsearch/Search2.vue

Test plan

• Open #/Search2?q=water and verify pagination controls appear.
• Change page and confirm URL updates with page and results update accordingly.
• Change page size and confirm URL limit updates and page resets to 1.
• Apply/remove filters and verify page resets to 1.
• Open #/Search2 (empty keyword) and verify results are shown (not blank/no-results).
• Reload on a deep link (e.g., #/Search2?q=water&page=3&limit=50) and verify state and results are restored.