feat: migrate Claude common config snippet from localStorage to config.json

Migrate the Claude common config snippet storage from browser localStorage
to the persistent config.json file for better cross-device sync and backup support.

**Backend Changes:**
- Add `claude_common_config_snippet` field to `MultiAppConfig` struct
- Add `get_claude_common_config_snippet` and `set_claude_common_config_snippet` Tauri commands
- Include JSON validation in the setter command

**Frontend Changes:**
- Create new `lib/api/config.ts` API module
- Refactor `useCommonConfigSnippet` hook to use config.json instead of localStorage
- Add automatic one-time migration from localStorage to config.json
- Add loading state during initialization

**Benefits:**
- Cross-device synchronization via backup/restore
- More reliable persistence than browser storage
- Centralized configuration management
- Seamless migration for existing users

src-tauri/src/commands/config.rs

@@ -135,3 +135,39 @@ pub async fn open_app_config_folder(handle: AppHandle) -> Result<bool, String> {
 
     Ok(true)
 }
+
+/// 获取 Claude 通用配置片段
+#[tauri::command]
+pub async fn get_claude_common_config_snippet(
+    state: tauri::State<'_, crate::store::AppState>,
+) -> Result<Option<String>, String> {
+    let guard = state.config.read().map_err(|e| format!("读取配置锁失败: {e}"))?;
+    Ok(guard.claude_common_config_snippet.clone())
+}
+
+/// 设置 Claude 通用配置片段
+#[tauri::command]
+pub async fn set_claude_common_config_snippet(
+    snippet: String,
+    state: tauri::State<'_, crate::store::AppState>,
+) -> Result<(), String> {
+    let mut guard = state
+        .config
+        .write()
+        .map_err(|e| format!("写入配置锁失败: {e}"))?;
+
+    // 验证是否为有效的 JSON（如果不为空）
+    if !snippet.trim().is_empty() {
+        serde_json::from_str::<serde_json::Value>(&snippet)
+            .map_err(|e| format!("无效的 JSON 格式: {e}"))?;
+    }
+
+    guard.claude_common_config_snippet = if snippet.trim().is_empty() {
+        None
+    } else {
+        Some(snippet)
+    };
+
+    guard.save().map_err(|e| e.to_string())?;
+    Ok(())
+}