What is the impact of DROP SCHEMA on concurrent read only workloads in PostgreSQL?
DROP SCHEMA would attempt obtaining exclusive use of the schema first, so it would only actually manage to drop the schema when PostgreSQL is done retrieving data from ongoing queries. Further queries would likely be locked until the end of the transaction in your question.

Queries accessing tables in the prod schema may fail after this transaction is finished if they (queries or functions procedures) were compiled prior to the dropping and renaming of the schemas, but should be safe for queries from newly established connections.