PostgreSQL replication failover

Hello,

we are running postgresqlserver on s390 zLinux machines. The distribution is RedHat 7 and RedHat 8, so we do not have
themany x86 tools available. 

We always run 2 instances with a replication (streaming) async mode, the replica is in hot_standby and we use it for
read-onlyaccesses. About the setup we have the following question: 

How is an orderly failover accomplished? Our current procedure is.

1. primary stop
2. promote replica to primary
3. create standby.signal on old primary
4. change primary_conninfo on old primary
5. start old primary as new replica

Is this processing correct? Are there any other steps that simplify a failover? How can we be sure that all changes
havebeen transferred from the old master to the replica? 

thanks in advance