Update dependencies and enhance App component functionality

- Added new dependencies: @polkadot/util and @gear-js/api to package.json and example/package.json.
- Implemented a test function in App component to interact with GearApi for balance transfer.
- Updated transaction signing logic to support both raw and payload types.
- Refactored Wallet class to improve socket connection handling and transaction management.
- Enhanced WalletStore by removing unnecessary listener setup code.

example/package.json

@@ -10,6 +10,8 @@
     "preview": "vite preview"
   },
   "dependencies": {
+    "@gear-js/api": "^0.44.2",
+    "@polkadot/api": "^16.4.9",
     "react": "^19.1.1",
     "react-dom": "^19.1.1"
   },