Update a test extension, maybe $readNDocuments, so it (1) implements a rewrite rule that inspects the field dependencies from the dependency analysis state (via get_needed_fields) and folds the requested fields into the source stage (2) implements a rewrite rule that reads the filter (via get_filter) of any subsequent $match stages (identified via get_name) and folds it into the source stage.

Add or update the appropriate integration tests.