I think a schema will definitely be part of the source listing, either in the main programming language source code or in a some other file used to define or initialize the database. But I don't think it is software, any more than a protocol is software. Software does something.

One tricky aspect of this is that even if the schema itself as a higher level concept doesn't fit into any of those definitions, all existing instances of the schema are likely considered either source listings or documentation. So the instances are barred from release per se, and you can't ask the government to create new documents.