重组为 backend/clients/docs 三层结构，并清理 git 污染。

将后端迁入 backend/，完善根目录 .gitignore，删除误提交的 .mypy_cache 缓存文件。

Co-authored-by: Cursor <cursoragent@cursor.com>

clients/demo-client/start.sh

@@ -1,6 +1,6 @@
 #!/usr/bin/env bash
 # Start the standalone demo client page for LAN access.
-# Backend must be running first: docker compose up -d --build (in repo root)
+# Backend must be running first: cd backend && docker compose up -d --build
 # Usage: ./start.sh [port]
 
 set -euo pipefail