Refactor logging configuration to use AppData directory

- Updated config.example.json to set default log_file to null.
- Modified config.py to resolve log file paths relative to the AppData directory.
- Added methods to get default log directory and log file path in AppData.
- Ensured logging behavior is consistent whether a log_file is specified or not.

CONFIG_README.md

@@ -103,6 +103,13 @@ Z:\aN5PysnXIuRECzcRbvHkjL7g0\Hintergrund_Agravity.png
   - Options: `"DEBUG"`, `"INFO"`, `"WARNING"`, `"ERROR"`, `"CRITICAL"`
   - Default: `"INFO"`
 
+- **`log_file`** (string, optional): Path to log file
+  - If `null` or not specified: Logs to `%APPDATA%\webdrop_bridge\logs\webdrop_bridge.log` (Windows) or `~/.local/share/webdrop_bridge/logs/webdrop_bridge.log` (macOS/Linux)
+  - If relative path: Resolved relative to the app data directory (same as above location)
+  - If absolute path: Used as-is
+  - Default: `null` (uses AppData directory for permissions compatibility)
+  - ℹ️ **Important**: Logs are always stored in the user's AppData directory to ensure the app can write logs in both development and installed scenarios
+
 - **`enable_logging`** (boolean): Whether to write logs to file
   - Default: `true`