Is there a dataset, database or API as large as WorldCat that allows for search by library of congress call number?
WorldCat has two different interfaces. One allows you to search by LC Classification and one does not.
The first interface is the public one you get from https://www.worldcat.org/ :

This interface's Advanced Search does not have an option to search LC Classification or call numbers:

The second interface, OCLC FirstSearch, is available through subscription via your local academic or public library. You will need to access it from your academic institution or public library and log in with your institutional credentials or your library card:

This interface's Expert Search has an option to search the Library of Congress Call No.:

Type Q179 into the &quot;Search for&quot; box, select Library of Congress Call No. from the &quot;Indexed in&quot; dropdown, and click Search.
Results: