GH-110109: pathlib tests: store base directory as test class attribute (#113221)

Store the test base directory as a class attribute named `base` rather than
module constants named `BASE`.

The base directory is a local file path, and therefore not ideally suited
to the pathlib ABC tests. In a future commit we'll change its value in
`test_pathlib_abc.py` such that it points to a totally fictitious path, which 
will help to ensure we're not touching the local filesystem.