GH-83863: Drop support for using `pathlib.Path` objects as context managers (GH-104807)

In Python 3.8 and prior, `pathlib.Path.__exit__()` marked a path as closed;
some subsequent attempts to perform I/O would raise an IOError. This
functionality was never documented, and had the effect of making `Path`
objects mutable, contrary to PEP 428. In Python 3.9 we made `__exit__()` a
no-op, and in 3.11 `__enter__()` began raising deprecation warnings. Here
we remove both methods.