> takes extended file attributes like immutable bit

Just to clarify, immutable isn't an extended attribute. It's one of the flag values in a Linux inode, which is supported by some filesystems such as ext4. It's in the API as STATX_ATTR_IMMUTABLE from the statx() stx_attributes field.

> according to the man page, AT_EACCESS (effective_ids=True) and
> AT_SYMLINK_NOFOLLOW (follow_symlinks=False) are implemented in 
> the glibc wrapper by calling fstatat() instead. I presume 
> that's limited to the discretionary st_mode permissions

Apparently this is the case. For example, given 'spam.txt' is an immutable file:

    >>> os.access('spam.txt', os.W_OK)
    False
    >>> os.access('spam.txt', os.W_OK, follow_symlinks=False)
    True

The AT_EACCESS flag has the same limitations in Linux, when it's not ignored. This issue with AT_SYMLINK_NOFOLLOW and AT_EACCESS will be resolved with the next release of glibc [1] on Linux systems running kernel 5.8+, which has a new faccessat2 system call that supports the flags parameter. Maybe initially a pathlib.Path method that implements an access check doesn't need to support the follow_symlinks and effective_ids parameters.

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[1] https://sourceware.org/git/?p=glibc.git;a=commit;h=3d3ab573a5f3071992cbc4f57d50d1d29d55bde2