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/app_config.rs

@@ -95,6 +95,9 @@ pub struct MultiAppConfig {
     /// Prompt 配置（按客户端分治）
     #[serde(default)]
     pub prompts: PromptRoot,
+    /// Claude 通用配置片段（JSON 字符串，用于跨供应商共享配置）
+    #[serde(default, skip_serializing_if = "Option::is_none")]
+    pub claude_common_config_snippet: Option<String>,
 }
 
 fn default_version() -> u32 {
@@ -113,6 +116,7 @@ impl Default for MultiAppConfig {
             apps,
             mcp: McpRoot::default(),
             prompts: PromptRoot::default(),
+            claude_common_config_snippet: None,
         }
     }
 }