Update tdjson_example.py to a new clean structure.

[9v2]

I've been working with TDLib for a few personal projects and noticed the Python example could use some improvements to make it more accessible to newcomers. After struggling with some aspects of the example myself, I decided to rewrite it while keeping all the functionality intact.
The main changes:

- Restructured the code into a proper class to make it easier to reuse
- Added better error messages and prompts during the authentication flow
- Improved documentation so new users understand what each part does
- Added type hints for better IDE support
- Separated the authentication logic from the main loop for clarity

I just made it easier to understand and extend. The new version should be a drop-in replacement that works exactly the same way but with a cleaner structure.
I've been using this version in my own projects for a while now and it's been much easier to build on top of. Hope this helps other (soy)Python devs.

[levlam]

It is recommended to use the libraries mentioned at https://github.com/tdlib/td/tree/master/example#python instead of the example, but the changes looks good and significantly improve the example. Therefore, I will merge them after the next code update on Github.

[9v2]

Thank you for paying attention. I have also been working with Pytdbot back in time. It was great, but I also sometimes needed to use raw codes such as the example in the repository.