Implement Search and Filtering for MCP Servers

## Overview
Add comprehensive search and filtering capabilities to help users find servers quickly in large deployments.

## Business Value
As deployments grow, finding specific servers becomes difficult. Search and filtering are essential for usability at scale.

## Technology Stack
- Backend: Go, PostgreSQL full-text search
- Frontend: TypeScript, React, Next.js
- Database: PostgreSQL GIN indexes, tsvector
- UI: Search components, filter chips, URL state management

## Skill Level Required
- Intermediate
- Understanding of database full-text search
- Experience with React state management
- Knowledge of URL query parameter handling
- Performance optimization awareness

## Learning Opportunities
- Learn PostgreSQL full-text search implementation
- Understand search indexing strategies
- Practice building performant search UIs
- Gain experience with URL state management
- Learn about search result highlighting techniques

## Impact
This feature dramatically improves usability for large deployments. Contributors will learn about search implementation, a common requirement in modern applications, and performance optimization techniques.

## Current State
- Basic server listing exists
- No search functionality
- No filtering options

## Subtasks
- [ ] Implement full-text search
- [ ] Add filter by status
- [ ] Add filter by type
- [ ] Add filter by tags
- [ ] Implement date range filtering
- [ ] Add sorting options
- [ ] Create search UI component
- [ ] Add search result highlighting

## Implementation Steps
1. Add search to backend repository methods
2. Implement PostgreSQL full-text search
3. Add filter parameters to API endpoints
4. Create search UI in frontend
5. Add filter chips and controls

## Getting Started
1. Review existing server listing code
2. Study PostgreSQL full-text search documentation
3. Check frontend component patterns
4. Review URL state management in Next.js

## Acceptance Criteria
- [ ] Full-text search works across server names and descriptions
- [ ] Multiple filters can be combined
- [ ] Search results are highlighted
- [ ] Filters persist in URL
- [ ] Search is performant (<100ms)
- [ ] UI is intuitive and accessible

## Estimated Effort
- Hours: 12-16
- Complexity: Medium

Review the existing server listing code, backend repository methods, API endpoints, frontend component patterns, and URL state management in Next.js. Done means combined search and filters work, results are highlighted, filters persist in the URL, performance stays under 100ms, and the UI is intuitive and accessible.

索引モデルが issue の本文から書いたものです。