refactor: rename search-server to mcp-server throughout codebase

- Updated all documentation references from search-server to mcp-server
- Removed legacy search-server.cjs file
- Updated debug log messages to use [mcp-server] prefix
- Updated build output references in docs

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

docs/public/architecture/search-architecture.mdx

@@ -397,7 +397,7 @@ Claude translates to appropriate API call.
 
 ### For Developers
 
-**Deprecated**: MCP search server (`src/servers/search-server.ts`)
+**Renamed**: MCP server (formerly `search-server.ts`, now `src/servers/mcp-server.ts`)
 - Source file kept for reference
 - No longer built or registered
 - MCP configuration removed from `plugin/.mcp.json`

docs/public/configuration.mdx

@@ -82,7 +82,7 @@ ${CLAUDE_PLUGIN_ROOT}/
 │   ├── summary-hook.js     # Summary generation hook
 │   ├── cleanup-hook.js     # Session cleanup hook
 │   ├── worker-service.cjs  # Worker service (CJS)
-│   └── search-server.cjs   # MCP search server (CJS)
+│   └── mcp-server.cjs      # MCP search server (CJS)
 └── ui/
     └── viewer.html         # Web viewer UI bundle
 ```

docs/public/development.mdx

@@ -33,7 +33,7 @@ The build process uses esbuild to compile TypeScript:
 
 1. Compiles TypeScript to JavaScript
 2. Creates standalone executables for each hook in `plugin/scripts/`
-3. Bundles MCP search server to `plugin/scripts/search-server.cjs`
+3. Bundles MCP search server to `plugin/scripts/mcp-server.cjs`
 4. Bundles worker service to `plugin/scripts/worker-service.cjs`
 5. Bundles web viewer UI to `plugin/ui/viewer.html`
 
@@ -41,7 +41,7 @@ The build process uses esbuild to compile TypeScript:
 - Hook executables: `*-hook.js` (ESM format)
 - Smart installer: `smart-install.js` (ESM format)
 - Worker service: `worker-service.cjs` (CJS format)
-- Search server: `search-server.cjs` (CJS format)
+- MCP server: `mcp-server.cjs` (CJS format)
 - Viewer UI: `viewer.html` (self-contained HTML bundle)
 
 ### Build Scripts
@@ -342,7 +342,7 @@ npm test
 
 ### Adding MCP Search Tools
 
-1. Add tool definition in `src/servers/search-server.ts`:
+1. Add tool definition in `src/servers/mcp-server.ts`:
 
 ```typescript
 server.setRequestHandler(CallToolRequestSchema, async (request) => {

docs/public/troubleshooting.mdx

@@ -542,7 +542,7 @@ The skill includes comprehensive diagnostics, automated repair sequences, and de
 
 2. Verify search server is built:
    ```bash
-   ls -l plugin/scripts/search-server.js
+   ls -l plugin/scripts/mcp-server.cjs
    ```
 
 3. Rebuild if needed: