PostgreSQL: Best practises for Deleting huge volume of Data in Replicated Environment

We have a prod database (PostgreSQL13) with a hot-standby(physical replication) as well as logical replication to a different subscriber server. Now we are in requirement of purging few year's record from some tables each having nearly 3-4M records for a month. All of these tables have timestamp field as well as PK and quite a few indexes. Considering the WAL rate and possible replication lag what are the best solution to perform deletes in such an environment with minimal impact to client queries?