You cannot connect to the Primary while connected to the Replica, except via postgres_fdw. Even then, it might not work, since the replica replicates _fdw definitions.
Start by looking at the current WAL LSN and insert LSN. The pg_current_wal_lsn is the location of the last write. The pg_current_wal_insert_lsn is the logical location and reflects data in the buffer that has not been written to disk. There is also a flush value that shows what has been written to durable storage.