[...]

This passage in PEP 563 appears not true in Python 3.9 with __future__ annotations, emphasis mine:

The get_type_hints() function automatically resolves the correct value of globalns for functions and classes. It also automatically provides the correct localns for classes.

If this passage was true, I believe the issue that resulted in my affixing type hints could have been averted.

As you've discovered, this is one of the places where PEP 563 seems to be out-of-date with respect to its implementation.  I sifted through the source code to typing.get_type_hints() twice, and near as I can figure out, localns is literally only ever set to None unless you override it with the parameter.