Enhance private handlers structure and add database support

- Introduced a new `PrivateHandlers` class to encapsulate private message handling logic, improving organization and maintainability.
- Added new dependencies in `requirements.txt` for database support with `aiosqlite`.
- Updated the private handlers to utilize modular components for better separation of concerns and easier testing.
- Implemented error handling and logging for improved robustness in message processing.

requirements.txt

@@ -1,6 +1,9 @@
 # Core dependencies
 aiogram~=3.10.0
 
+# Database
+aiosqlite~=0.20.0
+
 # Logging
 loguru==0.7.2