Remove ASDF serialization support from this package (deprecated in v5.1)

[eslavich]

Description

Over in https://github.com/astropy/asdf-astropy we are re-implementing astropy's ASDF support using the asdf package's new extension API. Once that package is finalized and released we can remove most ASDF-related code from astropy itself.

astropy.io.misc.asdf was deprecated in v5.1:

• Deprecate asdf support in astropy #12903
• Move skycoord test helper to non-deprecated location and use asdf-astropy Table connector #12930

TODO:

• Remove astropy/io/misc/asdf/ tree.
• Remove remaining usage of astropy.io.misc.asdf in this package.
• Remove astropy.io.misc.asdf docs.
• Replace optional dependency asdf with asdf-astropy and set appropriate minversion for that.
• Remove asdf from astropy/utils/compat/optional_deps.py, if possible.
• Remove ignored asdf deprecation warnings in setup.cfg.
• Update CI matrix accordingly.
• Also address DOC: Replace asdf extension "legacy" doc with new way of doing things #11899

[pllim]

I think #11899 is a subset of this work.

[eslavich]

I imagine we'll want to move most of that to asdf-astropy documentation and simply link there from here.

[pllim]

@eslavich , @nden et al. Is this really happening in 5.0? If not, please remove the milestone. Thanks!