Common backend code packages for Solr integration

There's a lot of shared code between the person search, business search, and newer namex search for solr integration. This ticket is to look at all 3 projects and pull out common code into its own modules (similar to the business common code in the lear repo)

Compare the person search, business search, and namex search Solr integration code, then review the business common code in the lear repo as the stated precedent. Identify repeated backend code and define shared modules that preserve each project's behavior. Done means the common code is extracted across all three projects and their existing Solr searches still work.

Written by the indexing model from the issue text.