Earlier quoted context omitted.
That seems to be just metadata about metadata. Where do you go to actually find the Classifications or Subject Headings themselves, in whatever format?
https://id.loc.gov/download/ offers bulk downloads of many of the vocabularies, including the subject headings. In addition, individual records of various types can be search for.
That seems to have Subject Headings, but not the Classification, unless I'm blind (a fairly high likelihood).
I've spent quite some time poking around the LoC website over the years without finding anything more accessible than the PDFs of the Library of Congress Classification. Are you aware of that being generally available?