Drupal's contrib module Search Restrict is a lightweight module that just does the basics - it allows administrators to restrict by role who can search for each content type.
From the module's page:
Approach of this module is to re-write the search query, so that
content is indexed and available as search results to users in role(s)
that have permissions to view it, but not displayed to other roles.
Integrates with Apache Solr to exclude results based on the role of
the person searching.
Simply download, install, and enable the module. Then to restrict (by role) which users can search which content types, edit each Content Type individually and there will now be a 'Search Restrict' section option (below the Display Settings). It allows you to specific, for each content type, which roles can search nodes of that content type.