It should not. The plugin keeps its data in its own tables rather than in postmeta, matches targeting rules in a single indexed query however many schemas you have, and caches rendered markup. The check of every page runs in WordPress's scheduled tasks, for about ten seconds at a time, and never on a visitor's page view. Saving a post checks that one post at the end of the save.
The work on a cached request is one indexed lookup. Pages that are not found share one cached copy, so a crawler asking for thousands of missing addresses costs one lookup each.
In the admin, the post and page editor loads one small stylesheet for the Schema Pro box and nothing else. The media library is loaded only on the screens where you choose an image: Site Identity, a schema's editor and the setup.
Still stuck? Ask the developers who wrote it. We aim to reply within one business day.
