Create an APE that describes the extent to which Astropy should be typed and the process for doing so

There has been a fantastic discussion in https://github.com/astropy/astropy/issues/15170 about the adding type hint annotations to Astropy. Given the magnitude of this change, we would probably benefit from an APE that answers questions like:

- To what extent should Astropy be typed? Should we strive for [mypy](https://mypy-lang.org/) regular mode or aim for mypy strict mode?
- How do we deal with existing mypy errors?
- What is the process for adding type hint annotations to Astropy?
- How would we go about adding mypy to the suite of continuous integration checks?
- How do we ensure that new code is typed?
- Should we require mypy strict mode for all new code or modules?
- How do we deal with dynamically created content? For example, do we add a `.pyi` type stub file for the individual units in `astropy.units`?

We could also add some helpful information, like which tools we could start off using. We probably don't want to be overly prescriptive, since the tooling landscape will probably change significantly in a few years.

Start by reading the linked discussion in astropy/astropy#15170, then review the existing APEs in this repository for structure and process. Draft an APE that addresses the listed typing scope, error handling, CI, new-code requirements, dynamic content, and tooling questions; done means the proposal is complete and ready for project review.

Written by the indexing model from the issue text.