fix: resolve incomplete search results in sessions tab

[iborazzi]

What does this PR do?
This PR resolves issue #61418. The current implementation of the Sessions tab search was page-local, meaning it only filtered the currently loaded set of 20 sessions instead of searching across the entire database. This fix updates the search logic to render full search results directly when a query is active, mapping them to the expected SessionInfo format.

Related Issue
Fixes #61418

Type of Change
[x] 🐛 Bug fix (non-breaking change that fixes an issue)

[ ] ✨ New feature (non-breaking change that adds functionality)

[ ] 🔒 Security fix

[ ] 📝 Documentation update

[ ] ✅ Tests (adding or improving test coverage)

[ ] ♻️ Refactor (no behavior change)

[ ] 🎯 New skill (bundled or hub)

Changes Made
web/src/pages/SessionsPage.tsx:

Introduced searchResultSessions as the primary list source when a search query is active.

Implemented mapping logic to convert SessionSearchResult objects into SessionInfo shape, providing necessary fallbacks for fields not present in search results (e.g., is_active, message_count).

Decoupled search rendering from local pagination.

How to Test
Navigate to the Sessions tab in the dashboard.

Enter a search term that exists in multiple sessions across the database (e.g., "hindsight").

Verify that the UI displays all matching sessions, rather than only those present in the first page of the default session list.

Checklist
[x] I've read the Contributing Guide

[x] My commit messages follow Conventional Commits

[x] I searched for existing PRs to make sure this isn't a duplicate

[x] My PR contains only changes related to this fix

[ ] I've run pytest tests/ -q and all tests pass

[ ] I've added tests for my changes

[x] I've tested on my platform: Windows 11

Documentation & Housekeeping
[x] I've considered cross-platform impact — N/A