In the initial implementation of plan caching, we saved the active
search_path when a plan was first cached, then reinstalled that path
anytime we needed to reparse or replan.  The idea of that was to try to
reselect the same referenced objects, in somewhat the same way that views
continue to refer to the same objects in the face of schema or name
changes.  Of course, that analogy doesn't bear close inspection, since
holding the search_path fixed doesn't cope with object drops or renames.
Moreover sticking with the old path seems to create more surprises than
it avoids.  So instead of doing that, consider that the cached plan depends
on search_path, and force reparse/replan if the active search_path is
different than it was when we last saved the plan.

This gets us fairly close to having "transparency" of plan caching, in the
sense that the cached statement acts the same as if you'd just resubmitted
the original query text for another execution.  There are still some corner
cases where this fails though: a new object added in the search path
schema(s) might capture a reference in the query text, but we'd not realize
that and force a reparse.  We might try to fix that in the future, but for
the moment it looks too expensive and complicated.