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`