Migrate to using DataStore

[snaik20]

Checklist

• I made sure that there are no existing issues - open or closed - which I could contribute my information to.
• I have read the FAQ and my problem isn't listed.
• I'm aware that this is a request for NewPipe itself and that requests for adding a new service need to be made at NewPipeExtractor.
• I have taken the time to fill in all the required details. I understand that the feature request will be dismissed otherwise.
• This issue contains only one feature request.
• I have read and understood the contribution guidelines.

Feature description

Migrate settings keys from traditional SharedPreferences to using DataStore once settings redesign is completed

https://developer.android.com/topic/libraries/architecture/datastore

Why do you want this feature?

DataStore offers a more modern, type-safe, and efficient approach to storing app data compared to traditional SharedPreferences. Its advantages in data flexibility, asynchronous operations, error handling, and integration with other Jetpack libraries make it the preferred choice for managing app data in modern Android development.

Additional information

Originated from discussion here: #10876 (comment)