I see there's currently no distinction between pathlib-internal attribute names and names that are free for third-party subclasses to use.
Should there be a stronger namespace for these, like _pathlib_sep, _pathlib_globber & _pathlib_stack?
Or should _sep & co. be documented so users know to not override them?

I suppose another option is to make them public as PurePath.separator and PurePath.is_case_sensitive

Hmm. What's the reason for removing sep from Parser, again? That's really the correct place for it.

Should there be a stronger namespace for these, like _pathlib_sep, _pathlib_globber & _pathlib_stack?

I guess that might be for another PR, since it affects _globber and methods as well.

I suppose another option is to make them public as PurePath.separator and PurePath.is_case_sensitive

Right, but then __init_subclass__ should only set them if they're not in __dict__.
It's probably best to keep them as private attributes. Or continue using @functools.cache to avoid magic leaking into the API -- e.g. here, you can't do:

class MyPath(PurePathBase):
    pass
MyPath.parser = MyParser()

All good points. Really my only motivation was to make the Parser interface method-only - partly so that issubclass() checks work, and partly for likely-misguided aesthetic reasons. You've convinced me it isn't a good idea, thank you for your feedback as ever!