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/lib/api/index.ts

@@ -5,5 +5,6 @@ export { mcpApi } from "./mcp";
 export { promptsApi } from "./prompts";
 export { usageApi } from "./usage";
 export { vscodeApi } from "./vscode";
+export * as configApi from "./config";
 export type { ProviderSwitchEvent } from "./providers";
 export type { Prompt } from "./prompts";