Migrate the example download from custom implementation to `ansys-tools-common`

Hi! I noticed that you are using a custom implementation to download examples from [example data](https://github.com/ansys/example-data) repository.

I suggest you to remove this implementation and use the implementation from [PyAnsys common tools](https://tools.docs.pyansys.com/version/stable/user_guide/ansys_downloader.html). The implementation is easily replaceable and it will save you maintenance work 🙂

Start by locating the custom implementation that downloads examples from the ansys/example-data repository, then compare its behavior with the ansys-tools-common downloader guide. The work is complete when the custom implementation is removed and example downloads use ansys-tools-common without breaking existing behavior.

Written by the indexing model from the issue text.